Hirzebruch homology [Elektronische Ressource] / vorgelegt von Augusto Minatta

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orgelegtINAhenUGURALMorb-atDISSERerTderA30.3.2004TIONergzuronErlangungMinattaderTDoktorwurdederHeidelbNaturwissenscvhaftlicvh-MathematiscDiplom-MathematikhenAugustoGesamaustfakultegnoagatmderundlicRuprecPrhufung:t-Karls-UniversitLauresHirzebruckhMatthiasHomologyDr.Gutach.c.hKrecter:Prof.Prof.GerdDr.Dr.forInbytrosignaturesductionndFortheaandiscretesagroupevvandZa(rationalacohomologyandclassertxis2alenceH(fundamenKwhile(vikConjecture.;,1);thatQb),classicalthecannothigherinsignatureordeterminedhigherbvytation-preservingx!isMthexcxharacteristic:nthatum=binercasesigThesexthe:NoxS;Oturinvariant.(oKand(toulation;iii1))tly!ectQh[arianceM.;reason,that]sig!ygroupwhereallLhomotop(arianMstudied)isZtheledLv-classulationofconjecture:Mo.orByHdenition,(theQsignaturehighersigdetermine1is(isMNo;conjecturestatemen)w=insuconlyandepvendsproponyMF.thisFoneurthermore,ysaccordingthetosignaturethexHirzebruchomotophinsignatureariantheorem,iftheevnorienumhomotopbequiverf

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Published 01 January 2004
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orgelegt
INA
hen
UGURAL
Morb
-
at
DISSER
er
T
der
A
30.3.2004
TION
erg
zur
on
Erlangung
Minatta
der
T
Doktorw



urde

der
Heidelb
Naturwissensc
v
haftlic
v
h-Mathematisc
Diplom-Mathematik
hen
Augusto
Gesam
aus
tfakult
egno

ag
at
m
der
undlic
Ruprec
Pr
h
ufung:
t-Karls-Univ
ersitLaures
Hirzebruc
k
h
Matthias
Homology
Dr.
Gutac
h.c.
h
Krec
ter:
Prof.
Prof.
Gerd
Dr.
Dr.for
In
by
tro
signatures
duction
nd
F

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the
a
an
discrete
sa
group
ev

v
and
Z
a
(
rational
a
cohomology
and
class
ert
x
is
2
alence
H



(
fundamen
K
while
(
vik

Conjecture.
;
,
1);
that
Q
b
),
classical
the
cannot
higher
in
signature
or
determined
higher
b
v
y
tation-preserving
x
!
is
M
the
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c
x
haracteristic
:
n
that
um
=
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er
case
sig
These
x
the
:
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;
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tur

invariant.
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o
K
and
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to

ulation
;
iii
1))
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ect
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h
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ariance
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.
;
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ery
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;
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group
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-class
ulation
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o
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denition,
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statemen
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urthermore,
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theorem,
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orien
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ery
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t,
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also
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class
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tro
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uous
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-theory:

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een
transformation
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b
wn
to
that
),
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whic
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vik
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o
(
v
in
conjecture
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equiv

alen
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t
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to

the
)
assertion
b
that
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the
This
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M
bly
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is
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e
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of
injection,
denote
and
].
th
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e
an
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in
])
tegral
Hirzebruc
v
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ersion
for
of
an
the
f
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y
vik

o
=
v
2
conjecture
1))
can
)
b
4
e
b
obtained
homomorphism
b

y
(
requiring
hh
the
)
assem
the
bly
for
map
orien
to
M
b
maps
e
class
an
id
in
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tegral
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split
elemen
injection.
([
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])
w
(
e
h
w
the
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tal
t
,
to
w
discuss
simplicit
here
[
is

a
X
more
con
geometrical
then
and
b
in
;
tuitiv
elemen
e
([
approac
hh
h
).
whic
fundamen
h
said
has
homotop
b
arian
een
discrete
suggested
if
recen
orien
tly
equiv
b
N
y
for
Matthias

Krec
K
k.
1)
Krec

k's
N
idea
f
is
n
to

in
(
tro
n
duce

a
n=
homology
Let
theory

hh
e

group
(
u
),
:
whic
S
h

he
M
calls
!
Hirzebruc

h
M
homology
induced
,
y
and
natural
whic
u
h
an
has
-dimensional
the
ted
follo
ifold
wing
.
fundamen
homomorphism
tal
the
prop
ordism
ert
[
y:
;
1.
]
there

is
O
a
(
natural
)
transformation
the
u
t
:

M
S
id
O
2

n
(
M
)
whic
!
w
hh
call

Hirzebruc
(
fundamen
)
class
2.
M
there
and
is
h
an
e
isomorphism
for

y
:
y
hh
M

If
(pt)
:
'
!
!
is
Z
y
[
tin
t
map,
]
w
suc
indicate
h
y
that
M
the

follo
the
wing
t
diagram

comm
M
utes:
2

n
S
X
O
The

h
u
tal

is
!
to
hh
e

y
(pt)
v
Z
t
[
a
t
group
]
,

for
#
y

tation-preserving

y
Here
alence

:
is
!
the
and
ring
an
homomorphism
map

:
:
!

(
S
;
O
[

;
!
]
Z
[
[
;
t

]
]
[
hh
M
(
n
(
]
;
!
sig