Spectral Sequences Attempt 2
Topological spaces
X tapspace 2 ex subspace
Hnlx 2nextBINf
2n'txt elmt.fcnlxls.t.dxecn.CH
similarly comply part of Itwhose
cheeses can be represented as cyclessoppnted
in Z lie in of Hula in theCx
Cunxin d Cit
cnn.it Zn Z Hutt
1st approximate of Hux quot is nota t
prtfromHut
approx pot fr in Hit Hut
app partfr quit is 2
B n LX
H'nLD C Hnk o s th run NuttyIdessupp in Z
o CCA CCN c O
l I l
ax
LIESHnlZ1 Hula Hnk H
va
Hn i 71IntelX 7
in general considera filtration f sols
X a X c c Xu X
Fi thx partsupported in Xi
i e iz f HnXi
FiHnXF flux
what's a spectral sequenerunindexed
Det A spectral segue in Ais a
soggy
r dr r drier Er eudemmphm
di o
t gettin l i sans H l Edd Ent
with train dives
121 A speed segue afhomological type is
a family of objects Ekg r
andmorphisms dfg i Efiq EF r qtr I
g f di o i hare is onsrtt Kr InaF pro indptrg rt I
a ptg h
a
121 A spectral segue ofchronological type is
a family of objects Er aPio
andmorphisms dri E'Yo Eprtr 8rt I
g f di o i hare isons
E b la dir t l p r qtr 1
in dirapio
Efriot BYE er s Z'T la dr
Bree Zitor
2 r YBrp.co E inby conesp thin hare BYE C Z In
in EPI
Br 43 c czn.fi czr's
sin cnn.to Iiiin E
Br bcBY.ir cBn9rtec cziiiitzczn.ii.CZ
B Irn Bai zig I 2airF fo ZEYB
Ingenal gnu A A subquot IA
As A
c
Ait Bi Ici
Ci ie Bi ie Ai i
Az Bye C c B CA
C CB CA Bye C AyeByeEko
Coc E c B eBo
Det we say Erpis bonded if fr all n
onlyIntely many terms Efg ptg n are
nonzero
in this case Bg stabilize aft fuk meh
zar
itsteps
Pig
Definite we saythat a spechlaq EEpig d
conizes to Hn nez Girl to a fitterCFpHn ftp.t n
nokknEpa.g 7Hptg ifwe are gun isms ftp eFptlptqFpiHptf
oftenwill seeEpa Hn
SimilarlyEPI H 8
means he
a filtration
E fPt H E F H EFP H E
s t E j6 F H fpHHpt8
iEa E EEG
E E FEo
of o
Fpig Hpso
E I E
F E5 Eo Eo oz O
G Eof H Ego o
zF l O
z L EFo 0F z o Eo H
aF2 X G
2,0o H2
FA IO
or F th EE Ef H E o
