非交换几何

所属分类:数学  
出版时间:2008-6   出版时间:世界图书出版公司   作者:孔涅   页数:661  
Tag标签:数学,Mathematics,计算机科学  

前言

  This book is the English version of the French “Geometrie non commutative” published by InterEditions Paris (1990). After the excellent initial translation by S.K. Berberian, a considerable amount of rewriting was done and many additions made, multiplying by 3.8 the size of the original manuscript. In particular the present text contains several unpublished results.  My thanks go first of all to Cecile whose patience and care for the manuscript have been essential to its completion. This second version of the book greatly benefited from the modifications suggested by many people: foremost was Marc Rieffel, but important contributions were made by D. Sullivan, J.-L. Loday,J. Lott, J. Bellissard, P. B. Cohen, R. Coquereaux, J. DLxmier, M. Karoubi, P. Kree,H. Bacry, P. de la Harpe, A. Hof, G. Kasparov, J. Cuntz, D. Testard, D. Kastler,T. Loring, J. Pradines, V. Nistor, R. PIymen, R. Brown, C. Kassel, and M. Gerstenhaber, with several of whom I have shared the pleasure of collaboration.  Patrick Ion and Arthur Greenspoon played a decisive r61e in the finalisation of the book, clearing up many mathematical imprecisions and considerably smoothing the initial manuscript. I wish to express my deep gratitude for their generous help and their insight.  Finally, my thanks go to Marie Claude for her help in creating the picture on the cover of the book, to Gilles who took the photograph, and to Bonnie Ion and Francoise for their help with the bibliography. Many thanks go also to Peter Renz who orchestrated the whole thing.

内容概要

his book is the English version of the French “Geometrie non commutative” published by InterEditions Paris (1990). After the excellent initial translation by S.K. Berberian, a considerable amount of rewriting was done and many additions made, multiplying by 3.8 the size of the original manuscript. In particular the present text contains several unpublished results.

书籍目录

TABIF
OF
CONTENTSPREFACEINTRODUCTIONI
NONCOMMUTATIVE
SPACES
AND
MEASURE
THEORY1.
Heisenberg
and
the
Noncommutative
Algebra
of
Physical
Quantities
Associated
to
a
Microscopic
System2.
Statistical
State
of
a
Macroscopic
System
and
Quantum
Statistical
Mechanics3.
Modular
Theory
and
the
Classification
of
Factors4.
Geometric
Examples
of
yon
Neumann
Algebras:
Measure
Theory
of
Noncommutative
Spacesα
Classical
Lebesgue
measure
theoryβ.
Foliationsγ.
The
von
Neumann
algebra
of
a
foliation5.
The
Index
Theorem
for
Measured
Foliationsα.
Transverse
measures
for
follationsβ.
The
Ruelle-Sullivan
cycle
and
the
ELder
number
of
a
measured
foliationγ.
The
Index
theorem
for
measured
foliationsA.
Appendix:
Transverse
Measures
and
Averaging
SequencesB.
AppendL,
c
Abstract
Transverse
Measure
TheoryC.
Appendix:
Noncommutative
Spaces
and
Set
TheoryII.
TOPOLOGY
AND
K-THEORY..1.
C*-algebras
and
their
K-theory2.
Elementary
Examples
of
Quotient
Spacesα.
Open
covers
of
manifoldsβ.
The
dual
of
the
infinite
dihedral
group
F
=
Z
>~
Z/23.
The
Space
X
of
Penrose
Tilings4.
Duals
of
Discrete
Groups
and
the
Novikov
Conjecture5.
The
Tangent
Groupoid
of
a
Manifold6.
Wrong-way
Functoriality
in
K-theory
as
a
Deformationα.
The
index
groupoid
of
a
linear
mapβ.
Construction
off!
~
E(T*M
~
f*TN,
N)γ.
K-orientations
of
vector
bundles
and
mapsδ.
Wrong-way
functoriality
for
K-oriented
maps7.
The
Orbit
Space
of
a
Group
Action8.
The
Leaf
Space
of
a
Foliationα.
Construction
of
C*
(V,
F)β.
Closed
transversals
and
idempotents
of
C*
(V,
F)γ.
The
analytic
assembly
map/~
:
K.,r(BG)
-.
K(C*(V,F))...9.
The
Longitudinal
Index
Theorem
for
Foliationsα.
Construction
of
lnd(D)
~
Ko(J)β.
Significance
of
the
C*-algebra
Indexγ.
The
longitudinal
index
theorem10.
The
Analytic
Assembly
Map
and
Lie
Groupsα.
Geometric
cycles
for
smooth
groupoidsβ.
Lie
groups
and
deformationsγ.
The
G-equivariant
index
of
elliptic
operators
on
homogeneous
spaces
of
Lie
groupsδ.
The
K-theory
K
(C*
(G))
for
Lie
groupsε.
The
general
conjecture
for
smooth
groupoidsA.
Appendix:
C*-modules
and
Strong
Morita
EquivalenceB.
Appendix:
E-theory
and
Deformations
of
Algebrasα.
Deformations
of
C*-algebras
and
asymptotic
morphismsβ.
Composition
of
asymptotic
morphismsγ.
Asymptotic
morphisms
and
exact
sequences
of
C*-algebrasδ.
The
cone
of
a
map
and
half-exactnessε.
E-theoryC.
Appendix:
Crossed
Products
of
C*-algebras
and
the
Thorn
IsomorphismD.
Appendix:
Penrose
TilingsIII.
CYCLIC
COHOMOLOGY
AND
DIFFERENTIAL
GEOMETRYIV.
QUANTIZED
CALCULUSV.OPERATOR
ALGEBRASVI
THE
METRIC
ASPECT
OF
NONCOMMUTATIVE
GEOMETRYBIBLIOGRAPHYNOTATION
AND
CONVENTIONSINDEX

图书封面

图书标签Tags

数学,Mathematics,计算机科学


    非交换几何下载



用户评论 (总计22条)

 
 

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