Cohomology of Groups: Graduate Texts in Mathematics, cartea 87
Autor Kenneth S. Brownen Limba Engleză Paperback – 28 apr 2012
| Toate formatele și edițiile | Preț | Express |
|---|---|---|
| Paperback (1) | 403.56 lei 38-44 zile | |
| Springer – 28 apr 2012 | 403.56 lei 38-44 zile | |
| Hardback (1) | 535.15 lei 6-8 săpt. | |
| Springer – oct 1982 | 535.15 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781468493290
ISBN-10: 1468493299
Pagini: 324
Dimensiuni: 152 x 229 x 17 mm
Greutate: 0.48 kg
Ediția:1982
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 1468493299
Pagini: 324
Dimensiuni: 152 x 229 x 17 mm
Greutate: 0.48 kg
Ediția:1982
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics
Locul publicării:New York, NY, United States
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Public țintă
GraduateDescriere
As
a
second
year
graduate
textbook,Cohomology
of
Groupsintroduces
students
to
cohomology
theory
(involving
a
rich
interplay
between
algebra
and
topology)
with
a
minimum
of
prerequisites.
No
homological
algebra
is
assumed
beyond
what
is
normally
learned
in
a
first
course
in
algebraic
topology.
The
basics
of
the
subject
are
given
(along
with
exercises)
before
the
author
discusses
more
specialized
topics.
Cuprins
I
Some
Homological
Algebra.-
0.
Review
of
Chain
Complexes.-
1.
Free
Resolutions.-
2.
Group
Rings.-
3.
G-Modules.-
4.
Resolutions
of
Z
Over
ZG
via
Topology.-
5.
The
Standard
Resolution.-
6.
Periodic
Resolutions
via
Free
Actions
on
Spheres.-
7.
Uniqueness
of
Resolutions.-
8.
Projective
Modules.-
Appendix.
Review
of
Regular
Coverings.-
II
The
Homology
of
a
Group.-
1.
Generalities.-
2.
Co-invariants.-
3.
The
Definition
of
H*G.-
4.
Topological
Interpretation.-
5.
Hopfs
Theorems.-
6.
Functoriality.-
7.
The
Homology
of
Amalgamated
Free
Products.-
Appendix.
Trees
and
Amalgamations.-
III
Homology
and
Cohomology
with
Coefficients.-
0.
Preliminaries
on
?G
and
HomG.-
1.
Definition
of
H*(G,
M)
and
H*(G,
M).-
2.
Tor
and
Ext.-
3.
Extension
and
Co-extension
of
Scalars.-
4.
Injective
Modules.-
5.
Induced
and
Co-induced
Modules.-
6.
H*
and
H*
as
Functors
of
the
Coefficient
Module.-
7.
Dimension
Shifting.-
8.
H*
and
H*
as
Functors
of
Two
Variables.-
9.
The
Transfer
Map.-
10.
Applications
of
the
Transfer.-
IV
Low
Dimensional
Cohomology
and
Group
Extensions.-
1.
Introduction.-
2.
Split
Extensions.-
3.
The
Classification
of
Extensions
with
Abelian
Kernel.-
4.
Application:
p-Groups
with
a
Cyclic
Subgroup
of
Index
p.-
5.
Crossed
Modules
and
H3
(Sketch).-
6.
Extensions
With
Non-Abelian
Kernel
(Sketch).-
V
Products.-
1.
The
Tensor
Product
of
Resolutions.-
2.
Cross-products.-
3.
Cup
and
Cap
Products.-
4.
Composition
Products.-
5.
The
Pontryagin
Product.-
6.
Application:
Calculation
of
the
Homology
of
an
Abelian
Group.-
VI
Cohomology
Theory
of
Finite
Groups.-
1.
Introduction.-
2.
Relative
Homological
Algebra.-
3.
Complete
Resolutions.-
4.
Definition
of
?*.-
5.
Properties
of
?*.-
6.
Composition
Products.-
7.
A
Duality
Theorem.-
8.
Cohomologically
Trivial
Modules.-
9.
Groups
with
Periodic
Cohomology.-
VII
Equivariant
Homology
and
Spectral
Sequences.-
1.
Introduction.-
2.
The
Spectral
Sequence
of
a
Filtered
Complex.-
3.
Double
Complexes.-
4.
Example:
The
Homology
of
a
Union.-
5.
Homology
of
a
Group
with
Coefficients
in
a
Chain
Complex.-
6.
Example:
The
Hochschild-Serre
Spectral
Sequence.-
7.
Equivariant
Homology.-
8.
Computation
of
d1.-
9.
Example:
Amalgamations.-
10.
Equivariant
Tate
CohoMology.-
VIII
Finiteness
Conditions.-
1.
Introduction.-
2.
CohoMological
Dimension.-
3.
Serre’s
Theorem.-
4.
Resolutions
of
Finite
Type.-
5.
Groups
of
Type
FPn.-
6.
Groups
of
Type
FF
and
FL.-
7.
Topological
Interpretation.-
8.
Further
Topological
Results.-
9.
Further
Examples.-
10.
Duality
Groups.-
11.
Virtual
Notions.-
IX
Euler
Characteristics.-
1.
Ranks
of
Projective
Modules:
Introduction.-
2.
The
Hattori-Stallings
Rank.-
3.
Ranks
Over
Commutative
Rings.-
4.
Ranks
Over
Group
Rings;
Swan’s
Theorem.-
5.
Consequences
of
Swan’s
Theorem.-
6.
Euler
Characteristics
of
Groups:
The
Torsion-Free
Case.-
7.
Extension
to
Groups
with
Torsion.-
8.
Euler
Characteristics
and
Number
Theory.-
9.
Integrality
Properties
of
?(?).-
10.
Proof
of
Theorem
9.3;
Finite
Group
Actions.-
11.
The
Fractional
Part
of
?(?).-
12.
Acyclic
Covers;
Proof
of
Lemma
11.2.-
13.
The
p-Fractional
Part
of
?(?).-
14.
A
Formula
for
??(A).-
X
Farrell
Cohomology
Theory.-
1.
Introduction.-
2.
Complete
Resolutions.-
3.
Definition
and
Properties
of
?*(?)277.-
4.
Equivariant
Farrell
Cohomology.-
5.
Cohomologically
Trivial
Modules.-
6.
Groups
with
Periodic
Cohomology.-
7.
?*(?)
and
the
Ordered
Set
of
Finite
Subgroups
of
?.-
References.-
Notation
Index.