sine 1122 a chedelhyhindqnht - Colorado State...
Transcript of sine 1122 a chedelhyhindqnht - Colorado State...
Math 676 :Day "
← tea.
All kdtayut bundles are synpluhz & all manifolds are Lagrangian
Tf M"
' 3 a Ll w/ lad comb Ix , , . ,
, xD her a pout pen (meaning forG Hit IU, 4) is a word ohtatij
p& xi : 414 → IR is gim J xi ( 41 air . ,
a D= a :),
thenay I c-
TIMcan be written as
I = If5 ; dxi
fr qe 94 .
Bit th u st a pT
's 614 → 1122 "
1g , 5) - ( x. , .. ,xn
,5, , . in )
then (x , , . ,xn
,}, , . in ) Site load cooks on T
' ylu ).
& th } mhs Tt M into a man : Hd.
Eu betty in local wads.we a define the 2- from
w = I,
dxindci
hhih is girl to - da he ← Esidxi,& here B dyed
.
Morar,its obviously mdgite sine it corresponds
in ah and . pth H the still syyketnfem an1122
"
.
The fans w Balled the canonical sypbhz from anT'sM & a is the tautological fan or Lionville 1- fum .
of case,aeb tochedelhyhindqnhtfile ptlrdoie float cords .
,ht 1h33 the . Rthkohedg . tgh .
we define a & w in a cordite . fee way .
ht ¥pf HIS'
he the new project . Wea ape a pinkie y
a ( p.es) = (dtp ,}D} = 5 ° d this )
Here uhe Tpa, Htm )ditto
TPM
Think 'M ) Kitten
In other wks,
a,µ , ,( D= 5(1dI#}Dv ) fray ve Ip ,}M .
Then,
of case,
w= - da.
Pat : a ichaetntdf : Viner 'lM),
n'a =n
.
Wht desk } men ? Renter tht Its m Mae svth seeks f ¥m^'HIM) = T'sM
,so
T' M
xgnfnBt then
, m Baathup ,so in : silt 'm ) film )
& so µ&( a ) is aI - fm an M
.
pdf : We can just pre th , } pontuie ,so ht PEM ; the god is to shield )
,b) = mph) fray uetpm .
Bt now (u*kDpk) = amp, ldnpv) = dip , up ,( dup D= up ( ditpup , dup ✓ )
=
Mp (d ( ton ) pv )
= up ( d 11,D ,u )
= mph) .
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Now,the nifty thing Btht , w/ th . } machinery , aydiftomopkhfmflds to into a canonical syapkdomphsn
flheir cotrt badly as folks :
Tf M ,,Mzae n
. mtbb wltwtobgtl tfms a , .az an Them,,Tthmz & fim ,
→ M ,is a diffo
,Fun He new
lift
f⇐ : HM .
→ Ttmz
( p. , } , ) - ( p. , 52 )
the p .= ftp. ) & 5
,= (dtp ,M£ ( or
, ynwtf , es z=¢dfpD'T'
5,)
One on due th ) D really a ditto ; the only annoying bit is convincing yonvtftht f# & fit'
are Smooth .