3
L-"* S f ^..l tt^ H.":^- J "t trOoriti^'. Let o<q<f *it\ ?,1 ) -mni F lr ', L (Prr) i= 1 S Ccpcint i cec,l i Jt"r fU. ? - 1 rtca^'dl rc(6cc* f .o t\ /r ,,1 t - 1t l- L S'* lC",r)edt let +l*'r\-=l [ = (e) c Su( r) , ": [*:" ezl tt* H<. j^, * d i,^gcrrn -. ;",.r,1 (.s 1c6,1) 3"f+u- !1 Jrl) Prl t,5."I cn {"ivie.l kn,}- Pq",F'. wc- Fi.,J .^ Hcelo-a.-J r6\i tN) oF_ Lcg,t i..h H,=Grg 5.,.", I h-..Jt -l t'\,,- .*"[ ?frr-r rf , ]dT: +rt i'7 +k r"ri"Jrfi F" H ( afi") |o pi + c0r1F, ,..,kr. E , +, c\r1v & r" "1i trl'.-.-\ .\^rr 't !t t)fi,\ $ |t mori $ir "\^t) of tf C)R,) '*r0e'ti*\\' Tt-h LC g,1) ir 1in t\ wJ . i/ Th,r , \c I a^? )e 1 H, -- H.= Tu'il ir -l-gk ? -E- lco"Dt of I r( t (1,,.,\ . a" \ ta\tr 1rr'= \] ,n [ \-\..3 -e,.d :0\i++:) I (e ,*) e S) ) ta\'= l *\" 1 I tt,-) e S]l l+t" > l-\'\ iKt= (to,-1 "z\n'=#],1,=Ic.,-,\er\e=Gl [ta,-; eS) ) f*\'. l*\'\ i t^,= 1(t,*).2 \a=*I ,1,=[C],*)eLl,=,-; t{* 5fi.^-J c^rd t t - tr 5( \itti"7 ,F S}

Jtr F lr S /r S'* L - UCB Mathematics | Department of ...jchaidez/notes/lens_space_proofs.pdf · f =1e> (r' * f = ft = (.') \ T"*f S (c ,.^,Lfr-, r* e: r erc\/t

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L-"* S f ^..l tt^ H.":^- J "t

trOoriti^'. Let o<q<f *it\ ?,1) -mni F lr ',

L (Prr) i= 1S

Ccpcint i cec,l i Jt"r fU.

? - 1 rtca^'dl rc(6cc* f .o t\

/r ,,1t - 1t l- L

S'* lC",r)edt let +l*'r\-=l

[ = (e) c Su( r) , ": [*:"ezltt* H<. j^, * d i,^gcrrn -.

;",.r,1

(.s 1c6,1) 3"f+u- !1 Jrl) Prl t,5."I cn {"ivie.l kn,}-

Pq",F'. wc- Fi.,J .^ Hcelo-a.-J r6\i tN) oF_ Lcg,t i..hH,=Grg 5.,.", I h-..Jt -l t'\,,- .*"[ ?frr-r rf , ]dT:+rt i'7 +k r"ri"Jrfi F" € H ( afi") |o pi + c0r1F, ,..,kr.E , +, c\r1v & r" "1i trl'.-.-\ .\^rr 't !t t)fi,\ $ |t mori $ir "\^t)of tf C)R,) '*r0e'ti*\\'

Tt-h LC g,1) ir 1in t\

wJ .

i/

Th,r , \c Ia^?

)e1

H, --

H.=Tu'il ir

-l-gk ?

-E- lco"Dt of I

r(

t (1,,.,\ . a" \ ta\tr 1rr'= \] ,n [ \-\..3 -e,.d :0\i++:)I (e ,*) e S) ) ta\'= l *\" 1I tt,-) e S]l l+t" > l-\'\ iKt= (to,-1 "z\n'=#],1,=Ic.,-,\er\e=Gl

[ta,-; eS) ) f*\'. l*\'\ i t^,= 1(t,*).2 \a=*I ,1,=[C],*)eLl,=,-;t{* 5fi.^-J c^rd t t - tr 5( \itti"7 ,F S}

f =1e> (r' *f = ft = (.')\

T" S (c ,.^,L<J.*f eF ,4 >fr-, r*

r erc\/t o

e: L " "Lrrinr b ret'"ib/te =e- -- L o

c^of , JtM !r rc nr.! \"

(r,.-) = (t^"'a r r'o'q/r h)

t 1,1 l: ng+v1

1 ."f un W

/,J ( <

i,,,1Nl o.^., obgqlr...r'- -tn r-+ '.I :

Lcs,1):= */, , [,l-t,^. F, ,E i, iirlla.^rJ r1\itti3 $c Lca,1)' \nrr'k-L''

F, = {(+,.-\ e t't,\ ^s1(z\ e (o, }61.a.'' t 6'^ !"'r..<-l''l J' *^1" 'fi^- .r*io.,. .[-cr.. H, , r, it ir t*l*'i-"cr^;' U d^[o'7r]'

?-:J,i,:' .i::"'H:f

r-;-;'", ;';i.i^^ {r;'r* >r,orl\"1 r

T Lt" f cr, r\- *)"-..,.* c'Y\ \c "*..- L * t 14'L f'^ I"'-1-. l Jt '*,. i n

Fu= [t",-) €Hr\ "*1 (-\ e Lo,\/el 1.

'.2 Hi lt ,7 ": Z/f

"[ Y\*

(/r-\"u \ t I.. 9.)* (t')

li, 7-?Hi rT A cecv<- s'{ q"(t)

Firrt r{ ;;H\*J- +L i-..,Jc "f F, j -Q',

# FrcF, fl c\c.l\1 lt^,rr tz' F,(^r\"L.- iS ^. [o ,^\ d.q !ro"-,rgt"'t ^.) .

l^ +\* F^-J-'?IF.1 J'r'^'^'i', g, if 5i*^-t \ s.- ral 't 1o"

*t1 i "' i't2' - t ti| ' '''o.

tj 6-r-*i{1r, Cotttr) = S. tr^u fu

=a,n \^t

u^-l.r +L1;'.2 > ll

I

,*^rr )F,- afr,

qro:@@*igrott.^,|

, & ,nr.J.. il aCucw- c i.uti.,1 t^ \"ai|-L I +'-'>

n k"< r^a-a, d i^r.- 1 tl*,5 ,'t ,cLr)l t[,c] = 9[[,1 + .tI.F,"l , (1t\* ( t$.,')) -- [F,l '

sr^^v ar)oau,t ?) [rr)*(Ll'r1 )=-'-\ f .,.k Y a$tr,:{l . ":t ,^

Cr",) r2,): P{'*1^.t'

-)

F t [,1 *{ot6.,l , C1J* ( rr.,])

,/.

: f^r .

tr h-,

4

fl-@@4p--)@

T,i:;* f*,,? ar P,14 s'cevw @ = cx rrr+1 c''r+ ;a