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Notes on Discrete Morse Theory (2)

Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

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Page 1: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Notes on Discrete Morse Theory (2)

Page 2: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Riprendiame ha dim.

oh.

2 in male pm

ashntthixe.

.

Si for sequence di pas raggi done ad qui passe si pardons tutti i win Cm

de war are wiki e si cdbxxare candle M.

I cellnssanuh .

i guerdon

coppindiallediverse

.

Il nuovo preset iodine cancellable be ygnk

cellmatear '

,6

P

,

tutti i let he es come he E. e gulli denanomolar: info

r non pre mere bae eh.

we XP" '

elhwih .

avni mielke pi > In. At pas so success no

pens amor a were alle rmhnhdi non aitch.

e leave le shone.

Vado amati finch men

hero Ike alle minimal with he-

"Stucco"he alleaiHidee precede

. .

Grimaldiche le idle old Gado di ogura oh gate alle able war care shake abode

in precedence : THE'

.no pedi of a

,. i no ,

mln in puts are of z

pedi F r > p > a.

Page 3: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

HttSimo K -

- Kophas,-

-p Kt

le aronian of ceylon che ni ehime

e has Kio 2 Kiis . .. o his f- hit quell orirphdhh

.

a mimwm.

En che

siano

cellearticle

. Quli Kisii -

- hi; ' I %,

a,

,. .

.

, % * ;) am teo entity.

( powers mere et dinnerware

diverse) .

be hj be centromere We Kisii be Hi; .

( petrelli mere el.bbh.tw aijtn-ii.ci ) . ha ade Dj : Ki;

→ Kis ,la

mopperde

estrade hj a %,

,tnnihi l

-iehhihae penaggoel perianth .

A there he siicaknisu a partie the K *( he im inane eh. alle di dim O )

altercate sncuniheuehte le alle ra . Hi . . (Crisis -

- Kt ) tonite has, ,HETs oh# ,

h's Is. ,o Tss ohs . z ie air n' a

.

Ouimetphalanxpomare

beetle. Eg ,

commehim Kita )

-

④Kt e- an iobecglesse O :dimensional

,Chimenti retire mesegnire .

Page 4: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

dim ferrules #¥g. perinehnbnesnl # alle.

hit ipso

iudone I

,ellora

K = he to ki,

e per castration Ho = (Ke;) .

.

.

Per patio into i

owmimi he ⑦P

e 2 P " circle clean innka,

we gtsheni eh. K.

Gk one cruel one

AEI, RbiinimhirpnCm sianecritic .Pohai are supine

p menino punitile

.

Cemidnbnx th i ummmolkernmtimoninolixscnhi

the T

( owen tutti i

cunninghe amebae r an une cello while er '

- Ogmo oh.

em.

he lnghezte Apai 2K -th. mazo . Sie a = was di heh.

K.

I -

- O alloy hike le fee an 'so are withe

, gpue dime diene

cone accgpiake an une t '

. Qneshenltime a centraggone conhip,

qm.net

I ⇐hint) ha incident a un lehip, K I ,

ness critic.

che idek

Page 5: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

ok co inK .

{ Ez I,

7 am Lo e of yacon G, r, ) EM

.

i¥¥¥¥tmean .

sugliee or in mohe he EG ) si

amess imae mi commierearh -

- KTM

innit per or →a.

A there to '

ye in Ki,

o'

e- entice.

Quinol e e- mini male per G in kin ,.

Quixote il reneged a

Riaz central a e m' elke Gr ; n

. not che in Kin - is 5 ! non pni

mere frack di me tr" '

( elthnmh one dah the Torelli Located .

but elka pi e men ankleminimal ).

Page 6: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Nel penegfrb hi,

, et Ki

#, pom 'm pensee di foie prime il

cdlomamentb a ,r

. .

Omaha fr pass are de Kim

ad um carbine KK.

, e.

Kinta; r ah

' '

⇐ K'

Hop or due go y si

akene cauellandhey

-' 6 ) c 2 DP

-

-

SP- '

e alkanets a 2 y-471 -

- y- ' H )

A

yi'

&"

id ) .

Gee I' "

ny- 'AHI S

"

.pk#T/xeaqInpityedhpinhdySukpine wobtaoh e y ,ud seconds

-

Anne e' incidence di h'

of Icanh " I idaho da quelle

di r un k ( comme di burglar 1) Crit) pinquellerdi KH un h'

H'I

welhplicehe per . G :c ] -1C :O,]Kanako- in

7 am si egging um pro

r > a tri i passions vedne r,

criticIn Kip,

eliminate it

the2. r

,de

MT;

grind.

inapplicable- rink a Kii , per inshrine )

Page 7: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Di :::÷:÷:

mine..

I ciii I inhume diri galle inekka ok ) .

he y.co ,

Hp I 9,9 -

Syl) IsHp F .

Ittpfrryy) E'

⇒ Hpk ,r - xD

⇒ ⇐Hip , Goin,

at ) E It'm (20,20*1) µ€* )N Z

Hp. .@ a - EH)

Page 8: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Complexe oh ' Mene m chain courtesies .

A anello cemmhetiw con I. Gmiehnane my couple so oh ' cotten

di A.vneohli :

Css : → Cme. -Cali cm.a →

Assnmereme Ie Awe PIDl me uncle i Eustace liberi ) .

E- notte che egri A - medals D

naioh

.

terpenein same drinker

di meehl ich .ci :h 'm #guests

D= ④ iii. Di,

DEA. fi

thfhieme le Araby d- um elevate de D come

ten eh -_ le EA I ie. D= O }( de e- um inhale in A

,epmd

' delle feme

hersEs( a )

,a EA )

.

Page 9: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Quintile hers (file l ai ) n'

he Di '

- A. fi E Alka ;).

Consider '

aime A- meekli ( him 't. gennett) D dehah ' oh '

m indene oh ' generate fr ,- if ,

he decoupages D

in mnohli cilia '

: D= to ! .A . fi

Sia quiet ca dehehe d . heli gondii Am# { fi ,- if

.

4- he,

f b E rn :

26¥22We(b. a ) -a

, Wnba ) ⇐A.

a CErn . s

un work,e) ehhunineke motile fence ).

Gk D= Um rn,

an online penile indene

de es b ⇐ we$6.to inAll torsos ) )

tht m matching.

Mmcrxr e- un matching m r

Page 10: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Nc . a E.b) EM ellen : filtersletters 6) e

ii ) wzk.es/Einwrk bile in Awm@1).

Ahem,

who Citnfh ) -

- {

cern:a men accgpiaho } .

(Dfef . Ilcgleoo di Morse (em. .

27. ) i ohfwiho come

segue : EY ⑦⇐cities , A. a

27mi± I wcptp

.p

on ±& is ↳76 ,be#16, is - - - -

4amfly,

is d

p.

d, paamrhe alternate

Page 11: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Ilene up , E A e- determinate mad tens (d) . Cembhriaue il

camming p come coupon'm are oh'

ennexvefismIAF IAB,Ah

Funny.ee#tI*aq7mnkh...a?m*jm. .

And ,) eh hen

An AAn

Mle few b une indene de 2 , pi ,

@8)=ap .⇐

= e w CK,andAdab, ) -

- e p = awlbnea ) ,ea .

Page 12: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

( been definite penli As Ca,11 An

,

hers @all hers (b , ) ,ee

. ) .

k free a 9 one isemerfismi i

* i keai) = aviceit = aWti ,e!

. t

due l'

i meme e- in Athena ; ) EEAt Aski ) .

A there per elf.

ri he :

Wfp) i: e →k

fine ,

o Vr. o pin- a - - o yep ,

( E )

f Mel Coro libero,

si me where :

§ wetat

"

LIpwt .d) / p awing M

Page 13: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Prepotency She A PID e D um A. weekly

on geverehei f. ,

- - -

, flu e me ohceyenihlnein meehl . iclici

D= ¥.

A. f:

dem Anctil

Cdi) Kepner- A

.f¥A/µ§She g ,±fi

IIEfztEjzz c ; ,f ;eimmtib.lkmed hers fz{

Si -

- fit Csifz i =3 ,- - - ik

un elke inanbne d . genuehei oh - D,

Cen le

there heroine hers ( file'Tendril , Ii "

in .

Page 14: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

A there si he me ehcaperihbe

D=¥EAohh I lierne he i gi suo Sweeten'

, quinol '

e cane

dime there de

E ai fi = O, ai EA

,i -

- I.

-- in

,

⇒ ai E tous fi ) -

Ssh . travels an

'

there

@at¥,

ai Ii ) f ,* Eezfat ¥ ,@it ez Ci ) fi -

- O

Page 15: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

he ate a ,E hers@I = this @z) .

Penile ottaviano ,

has,t Eisai Si = O e d '

consequence :

@at¥,

ai Cai ) f ,t ¥ ,ai fi -

- O

In di ai e hers Lfit .

tons @it ,i = B, K e pindi

a- a'

ni ohne ai

Q, f , = O

he di a.

c- teas @, ) ±tenth ).

-

Page 16: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Teenie She C* ,

2.

um couple see oh ' A - rneehhi,

um D= Urn gereetvi one prime e Mcr xD my

matching acidic del Khe describe. .She EM

, ,27.

il couples so

di Mease date soph .Attire

Haka ,2*)=H*( e'7.27. )I

ohne.

Orohwmbme le apple.hn M :

Pr -- ka, bi ) , Peter, 64 ,

- - -

, Pritam . but.

Sk M " ! { pi EM .

-

ish } ,no ,

- - - im . [ Mateo ,MM 'M ] .

lhbrennrhiMM e- acidic

.

he G* l' insinuated. element . criticper M ' "

.

Page 17: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

F academe meohifideancanineaill 'inn '

ene dei generation I.

Srypewhe In = I fnijj.se,- . .sn ,

M ? O-

At preen . who

ethene f "m,;

I perked.

fm, ; ,

con le theme Renderer.

He f :! = fu, ; ,

Um,

j . A summons m inehnhe

m K 30 oh .

over osthihe gereehei fkn? j ,hzo , per

e,

t.

c.

1) n'

he me oheupmvu.hr same dinette :

e*

= Are toga

.

A.fkn! ;fm ;

ohne Ar,

ai deanpene come

Page 18: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

An Pi

emends i oh ; sottocoylenieeiclici h elevated "

Pi : -for A.614? - Adi '- of

due I '

enenehme cattle e- hehe delle nettrplaomper W ( bi

, ai ) e printer i iconefvsne

2) It bade 2 induce m Cnr.

m berate 24

de I deke delle ferrule old Capano eh '

theme riyals I watching M ' ".

Page 19: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Per h -

-O si he Ao = O e 2 " ⇐ 2

.

Ceniehnbne Wht" = M " U { Cane, ,

6am)},

Pei di M """ e-

orifice,

ran i seu comin 'm' elhernenti in M

" ' forthe

,e and ,

ed eccrine di quelle bande bae, band .

Quiet il officiateet at"¥. in 2M 6mm,

e- vvlbm. ,

and: .One sesh turbine :

a "n!,

= 2 "ban!

,-

- www..am. ) d"

n . t E.EC/bmn.f%1fY

! fu ,jtGk

due iceefhrouts here slider 'Mihdhar delle

ferrule argue .

Page 20: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Sinets . de le terrine oh' a'Y?.

e- le hesse di e'Yen per

definite di watching ( e puhillimnagine at m elumhi he homme de

divide le hereby dell ' Iemhe ) .

One tf fm, ; E Cr * .

on n== dim loner, feed ane le

sesh. hmm :

b "i = b'"ne '

afkn! = Nhi - wow .

.am/eCaM.n. .2

"

f 'T! ) to !! ,

bin !iii. ; done ok.5 e- eattendee

'

Meine.✓ in 8" f"m;

whelkHI

9 htt

Page 21: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Rule qui : this fkn? ; = hers f"mj .

Per inherent elements leuiamo film!! = fMm,; .

A ppl. chiana be prepositive precedents an

f. = 6¥, , fz -

-amine

, ,e nmuarob sncaninonuho gli alki

f "n, c- Gr.

- fans ,bae,

) ; peniame :

s .-- fi , gz== 2 " 69!? ± adf.fi

e huh' Hi elkafcenamilkfemlehgnrn ,athenians

:

Page 22: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

C * ⇐ Ane.

④ftp..ca

. ,

A - FIT? on

A her = An ④ Phet

nude rn .-

. to - A6,9¥,'t

-aAah¥. →o

]-

- I

fkn"! = Phi - whom..am/eCaM.n...tfIH6!! ,

wtf :;! , ain't.

o Kuia"IIn e- idek )

eqwto ⇒ c f"It

,to 'T

'

O.

Page 23: Notes on Discrete Morse Theory (2) - unipi.itpeople.dm.unipi.it/.../DiscreteMorseTheory_2.pdf · Notes on Discrete Morse Theory (2) Riprendiame ha dim. oh. 2 in male pm ashntthixe

Per commute 2 ""cardie

,n' spoke a J"

,Seb Ar

quoi camninieltmnenti de cenheryeno il let Cana,

bn#Iide wi si doing be ferrule .