• Home

  • Documents

  • Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic...
53

Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,

  • Upload
    hathuan

  • View
    217

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 2: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 3: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 4: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 5: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 6: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 7: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 8: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 9: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 10: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 11: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 12: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 13: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 14: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 15: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 16: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 17: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 18: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 19: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 20: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 21: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 22: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 23: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 24: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 25: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 26: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 27: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 28: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 29: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 30: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 31: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 32: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 33: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 34: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 35: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 36: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 37: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 38: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 39: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 40: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 41: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 42: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 43: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 44: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 45: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 46: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 47: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 48: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 49: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 50: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 51: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 52: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,
Page 53: Notes on hyperbolic groups - City University of New Yorkmath.hunter.cuny.edu/olgak/hyperbolic groups/MSRInotes2004.pdfnotes on word hyperbolic groups j. m. alonso, t. brady, d. cooper,

Geometric structures and representations of discrete groups · Groups dividingΩ are never Gromov hyperbolic (Benoist [2004]); for d = 4 they are relatively hyperbolic ... 3.3 AdS

Geometric structures and representations of discrete groups · Groups dividingΩ are never Gromov hyperbolic (Benoist [2004]); for d = 4 they are relatively hyperbolic ... 3.3 AdS

Documents
Hyperbolic Geometry & Kleinian Groups · Hyperbolic Geometry & Kleinian Groups Author: Greg Jackson Supervisor: Dr. Jesse Ratzkin Updated September 30, 2013. ii Plagiarism Declaration

Hyperbolic Geometry & Kleinian Groups · Hyperbolic Geometry & Kleinian Groups Author: Greg Jackson Supervisor: Dr. Jesse Ratzkin Updated September 30, 2013. ii Plagiarism Declaration

Documents
Hyperbolic manifolds, discrete groups and ergodic …people.math.harvard.edu/~ctm/home/text/class/harvard/275/...topological 3-manifolds Mare hyperbolic; that is, Mis homeomorphic

Hyperbolic manifolds, discrete groups and ergodic …people.math.harvard.edu/~ctm/home/text/class/harvard/275/...topological 3-manifolds Mare hyperbolic; that is, Mis homeomorphic

Documents
Quasiconvex Subgroups and Nets in Hyperbolic Groups

Quasiconvex Subgroups and Nets in Hyperbolic Groups

Documents
QUASI-HYPERBOLIC PLANES IN RELATIVELY HYPERBOLIC GROUPS

QUASI-HYPERBOLIC PLANES IN RELATIVELY HYPERBOLIC GROUPS

Documents
The Kadison-Kaplansky conjecture for word-hyperbolic groups · The Kadison-Kaplansky conjecture for word-hyperbolic groups Michael Puschnigg Institut de Math´ematiques de Luminy,

The Kadison-Kaplansky conjecture for word-hyperbolic groups · The Kadison-Kaplansky conjecture for word-hyperbolic groups Michael Puschnigg Institut de Math´ematiques de Luminy,

Documents
Coxeter groups, quiver mutations and hyperbolic manifoldsmaths.dur.ac.uk/users/anna.felikson/talks/refl-mut-man.pdf · Coxeter groups, quiver mutations and hyperbolic manifolds Anna

Coxeter groups, quiver mutations and hyperbolic manifoldsmaths.dur.ac.uk/users/anna.felikson/talks/refl-mut-man.pdf · Coxeter groups, quiver mutations and hyperbolic manifolds Anna

Documents
Integers, Modular Groups, and Hyperbolic Spacegeosym.mik.uni-pannon.hu/images/presentations/johnson.pdf · 2016-05-05 · Integers, Modular Groups, and Hyperbolic Space NORMAN W

Integers, Modular Groups, and Hyperbolic Spacegeosym.mik.uni-pannon.hu/images/presentations/johnson.pdf · 2016-05-05 · Integers, Modular Groups, and Hyperbolic Space NORMAN W

Documents
Quasiconvexity in Word-Hyperbolic Coxeter Groups

Quasiconvexity in Word-Hyperbolic Coxeter Groups

Documents
Conjugacy of finite subsets in hyperbolic groups

Conjugacy of finite subsets in hyperbolic groups

Documents
Bounded cohomology and isometry groups of hyperbolic spaces · Bounded cohomology and isometry groups of hyperbolic spaces Received August 5, 2005 and in revised form September 25,

Bounded cohomology and isometry groups of hyperbolic spaces · Bounded cohomology and isometry groups of hyperbolic spaces Received August 5, 2005 and in revised form September 25,

Documents
Free Kleinian groups and volumes of hyperbolic 3-manifolds · Free Kleinian groups and volumes of hyperbolic 3-manifolds James W. Anderson, Richard D. Canaryy, Marc Culler z,y, Marc

Free Kleinian groups and volumes of hyperbolic 3-manifolds · Free Kleinian groups and volumes of hyperbolic 3-manifolds James W. Anderson, Richard D. Canaryy, Marc Culler z,y, Marc

Documents
Elementary subgroups of torsion-free hyperbolic groups · 2014-10-05 · Elementary embeddings in hyperbolic groups Obtaining a non-injective reretractionp From reretractionp to hyperbolic

Elementary subgroups of torsion-free hyperbolic groups · 2014-10-05 · Elementary embeddings in hyperbolic groups Obtaining a non-injective reretractionp From reretractionp to hyperbolic

Documents
Assembly Maps, K-Theory, and Hyperbolic GroupsKey words. Cyclic cohomology, elliptic group ¢ocycles, generalized assembly map, hyperbolic groups. Introduction The classical assembly

Assembly Maps, K-Theory, and Hyperbolic GroupsKey words. Cyclic cohomology, elliptic group ¢ocycles, generalized assembly map, hyperbolic groups. Introduction The classical assembly

Documents
Rational Embeddings of Hyperbolic Groups · of Gact on @ by transducers. Symbolic dynamics for actions of hyperbolic groups on their boundaries have been studied extensively (see

Rational Embeddings of Hyperbolic Groups · of Gact on @ by transducers. Symbolic dynamics for actions of hyperbolic groups on their boundaries have been studied extensively (see

Documents
ONE FAMILY OF HYPERBOLIC SPACE GROUPS WITH SIMPLICIAL DOMAINS

ONE FAMILY OF HYPERBOLIC SPACE GROUPS WITH SIMPLICIAL DOMAINS

Documents
Random Walks on Hyperbolic Groups III - University of …galton.uchicago.edu/~lalley/Talks/paris-talkC.pdf ·  · 2014-01-23Random Walks on Hyperbolic Groups III Steve Lalley University

Random Walks on Hyperbolic Groups III - University of …galton.uchicago.edu/~lalley/Talks/paris-talkC.pdf ·  · 2014-01-23Random Walks on Hyperbolic Groups III Steve Lalley University

Documents
HYPERBOLIC GEOMETRY, FUCHSIAN GROUPS, AND TILING …math.uchicago.edu/~may/REU2018/REUPapers/Olivares.pdf · HYPERBOLIC GEOMETRY, FUCHSIAN GROUPS, AND TILING SPACES 5 3.2. Groups

HYPERBOLIC GEOMETRY, FUCHSIAN GROUPS, AND TILING …math.uchicago.edu/~may/REU2018/REUPapers/Olivares.pdf · HYPERBOLIC GEOMETRY, FUCHSIAN GROUPS, AND TILING SPACES 5 3.2. Groups

Documents
One-Variable Equations Over Hyperbolic Groups

One-Variable Equations Over Hyperbolic Groups

Documents
Boundaries of hyperbolic groups - Department of Mathematics

Boundaries of hyperbolic groups - Department of Mathematics

Documents
Free groups - City University of New Yorkmath.hunter.cuny.edu/olgak/slides_lecture1.pdfFree groups Algebraic de nition An expression of the type w = s 1 i1:::s n in (s i j 2S; j 2f1;

Free groups - City University of New Yorkmath.hunter.cuny.edu/olgak/slides_lecture1.pdfFree groups Algebraic de nition An expression of the type w = s 1 i1:::s n in (s i j 2S; j 2f1;

Documents
Coxeter groups, hyperbolic cubes, and acute triangulations · 10/07/2013  · Coxeter groups, hyperbolic cubes, and acute triangulations S. Kim and G. Walsh July 10, 2013 Abstract

Coxeter groups, hyperbolic cubes, and acute triangulations · 10/07/2013  · Coxeter groups, hyperbolic cubes, and acute triangulations S. Kim and G. Walsh July 10, 2013 Abstract

Documents
Verbal subgroups of hyperbolic groups have in nite width

Verbal subgroups of hyperbolic groups have in nite width

Documents
Hyperbolic Groups Lecture Notesjim/samos.pdf · 2000. 10. 6. · Hyperbolic Groups Lecture Notes James Howie Heriot-Watt University, Edinburgh EH14 4AS Scotland J.Howie@ma.hw.ac.uk

Hyperbolic Groups Lecture Notesjim/samos.pdf · 2000. 10. 6. · Hyperbolic Groups Lecture Notes James Howie Heriot-Watt University, Edinburgh EH14 4AS Scotland [email protected]

Documents
Subgroups of Lacunary Hyperbolic Groups and Free Products · 2020-02-21 · Subgroups of Lacunary Hyperbolic Groups and Free Products Krishnendu Khan Abstract A nitely generated group

Subgroups of Lacunary Hyperbolic Groups and Free Products · 2020-02-21 · Subgroups of Lacunary Hyperbolic Groups and Free Products Krishnendu Khan Abstract A nitely generated group

Documents
AMENABLE HYPERBOLIC GROUPS C 1. Introduction 1 2. Preliminaries on geodesic

AMENABLE HYPERBOLIC GROUPS C 1. Introduction 1 2. Preliminaries on geodesic

Documents
Coxeter groups and hyperbolic manifoldsbje1/hyperbolic_coxeter.pdf · Coxeter groups and hyperbolic manifolds. obtained from by removing those nodes not in. S. and their incident

Coxeter groups and hyperbolic manifoldsbje1/hyperbolic_coxeter.pdf · Coxeter groups and hyperbolic manifolds. obtained from by removing those nodes not in. S. and their incident

Documents
Complex hyperbolic quasi-Fuchsian groupsjplatis/CHQF.pdf · 4 Complex hyperbolic quasi-Fuchsian groups complex hyperbolic geometry was hardly studied at all. Later, work of Chen and

Complex hyperbolic quasi-Fuchsian groupsjplatis/CHQF.pdf · 4 Complex hyperbolic quasi-Fuchsian groups complex hyperbolic geometry was hardly studied at all. Later, work of Chen and

Documents
Hyperbolic Ornaments - Drawing in Non-Euclidean Crystallographic Groups · 2009. 6. 10. · Hyperbolic Geometry Anatomy of the Hyperbolic Plane Definition (Hyperbolic Axiom of Parallels)

Hyperbolic Ornaments - Drawing in Non-Euclidean Crystallographic Groups · 2009. 6. 10. · Hyperbolic Geometry Anatomy of the Hyperbolic Plane Definition (Hyperbolic Axiom of Parallels)

Documents
Coxeter groups and hyperbolic manifolds - …bje1/everitt04b.pdf · Coxeter groups and hyperbolic manifolds 129 obtained from by removing those nodes not in S and their incident edges

Coxeter groups and hyperbolic manifolds - …bje1/everitt04b.pdf · Coxeter groups and hyperbolic manifolds 129 obtained from by removing those nodes not in S and their incident edges

Documents