Hirzebruch homology [Elektronische Ressource] / vorgelegt von Augusto Minatta

Description

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Sujets

• Mathematics

Informations

• Publié par: ruprecht-karls-universitat_heidelberg
• Publié le: 01 janvier 2004
• Nombre de lectures: 32
• Langue: English

Extrait

orgelegt
INA
hen
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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

or
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
!
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the
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:
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um
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er
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sig
These
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the
:
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o
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to

ulation
;
iii
1))
tly
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h
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ery
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>
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)

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-class
ulation
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o
.
or
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denition,
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statemen
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v
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.
this
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one
urthermore,
ys
according
the
to
signature
the
x
Hirzebruc
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h
in
signature
arian
theorem,
if
the
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n
orien
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er
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ery
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;
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ered
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and
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form
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of
,
general
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vik
all
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M
1);
;
)

the
)
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e
sig
d
1
x
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homotopy
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;
clear

the
)
vik
:
v
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is
general
rational
ho
t,
w
it
ev
ould
er,
e
the
teresting
higher
ha
signatures
e
do
in
also
form
dep
of
end
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on
approac
the
to
map
(
iv
class
In
h
tro
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duction
2
this
uous
question
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mak
the
es
man-
use
;
of
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L

-theory:

it
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t
b
O
een
transformation
sho
b
wn
to
that
),
the
whic
No
M
vik
[
o
(
v
in
conjecture
homotop
is
M
equiv

alen
M
t
u
to

the
)
assertion
b
that
n
the
This
assem
M
bly
n
map
u
is
hh
a
e
rational
of
injection,
denote
and
].
th
an
us
e
an
]
in
])
tegral
Hirzebruc
v
b
ersion
for
of
an
the
f
No
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
S
tegral
M
split
elemen
injection.
([
What
])
w
(
e
h
w
the
an
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