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Lecture 13 ; Tuesday tooth Farvardin 1399 .
#
P,so
t' n Ror- Simplex = ?
.
Citi - l Zeit Pier"
a
Ri=o
.
Pro
P.
- R. linearly independent .' P.
→oh
Pa
2- Simplex Las. Cop. -1919+919 I Cotcitczel , Ci ER-1 } .
- -
Barycentric coordinatesfoe .
%
• Pa→face .
Complex K { di } is if dick , Ojloi → g. EK-
2) if Oi , Oj Ek → bing.ie/OEQ.noje6i,6j
Def : face: if 8. ( P. ,% , R Pr ) → 8. - LP, R R) is a face f 8. e--
I 81=4919 R) is'
ansthufaufoacp.p.PK) Ps .
"simple et here, simplex .
€ "
④ GPD , 4919193, ( BBB) . (BBB) 2-faces
P. Pik
t - faces3-Simplex 4919 ) 4919) ( Pok) - - - .
(B) 49 ) CPD CB)O -face
:::i:÷:* .
K =L CP. 1919149191119191,49191, CRR) . ( 197,497,497,497,493}a- ma
@ BPD n E) = 49 ) ¥ Bk)
o , noo- een hot . oh
#-
yIT = { Oi , Or , 6, . - J . f. (K) = Jyj
Finitely generated abelian Gop .
Cr E GCK ) a. ⇐ a. ¢"
sie k
\r- chain
1%14914%1 and its faces} .
C. (K ) = { c. P. + after I a- EZ} .
Chain Groups.← / C
'( K) =L 90491%+949173+041919) I a. ez}
Crack) = I b. CREB) I b. EZ} .
C. ( K ) EZ-02*7 GCR) = ZAZIE acts = Z
⑧
Orientation : CBP, e) ELK; Ra Po.) if Lilia is as anevenpamttaf
- -
LD l r- i )
P ,°
/P.
. ok e- CB - - B) Jim E.&, I
• P,e.Is c'%
pr . l " " "
Here . Nj#-
GCK) : LRP.> ⇐ - EP. EBBE 19¥ - l Riki K:S
if Cci in ) is an odd
#penttf @ in D .
D : Cr CK )- Chick)-
r
dmdr= e- ein a complex f dimm n :
Crick) Crick) Crack)€s . - - C.We.cm
His -- Ij
" 963-08%1919> = eke> -CBR>+49197
2.2lb = epis-497 - ( < Rs-Cps) + (497-497)=0
thin : Omar - o proof .
. Or RP. - RATE.
⇐I' else E. Pm - e>
drier 40.19 Pr> = ¥.
( Tpi. . Hi ee -- E . En - - E. Rei - e>
+ ¥⇐,
l Pok Pi Piti B '
' Pac - - Pr>f .
- - -- - = .fi#ee.? ,
Ip,
Definition : c. = IT)÷,
c- GCK) K={ 1¥,
i -- J .
④ B) +49N
a'. go.TYg.pe, each
Dc,= d (CP. 197+49197) = Pop - Hot E- P, = R- B
DC,'=P, - P.
Zelda Kera e Crete ) FCK# { Cre Eck) I or -_ of .
↳ E Fck) 7 of Zick)
FCK) w a group . Prof : if 3 , ,2EZ . →
92=0 932=0 → dL3ie3u) -o → 3 , -132 C- Z (K)
Br =L be !!! !. .!:{"oh
p.
""
then ec.cn .
'
b'E- CRB>+ CBR>KRP,> E C, CK ) .
b =D BR) deep. Papi) ⇐ Cars - CP. KALBA>=
b't to ? a 49197+49197+47197
Question : es'
n an equivalence relation ?1) crncr - G- Cr-0=20 .
2) Cr- Cr'
- Cr- Cr' = @ Cre, → Cr'- Cr -0C - Cre .) - Cr
'- Cr
3) Crr Cri Cri - Cr "
ter- a. =3Crete. '- a'Ida;
Cr- Cr" =D ( Cratchit ) - Cr - C.
"
turn. -2k£.
=L "" ""'s
Ie.IIE
[ Cid + Ici ] I Crtci] .
{ - Ici se f - ah .
thick) ⇐ r-th homology Gopfk .
]
wig mix
if."
oa=o,a--a"
↳,
Definition : if f. K- X n'ahomeomojsafhxdgo.g.eg.ae.
'th Ks.
calkdatriangdihfx .
€?÷÷¥Q
Is