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Axiomatic K-theory for C*-algebras
Author:
Corneliu Constantinescu
ISBN:
978-1-940366-79-1
Published Date:
July, 2017
Pages:
288
Paperback:
$130
Publisher:
Science Publishing Group
OPEN ACCESS
Table of Contents
The Whole Book
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Front Matter
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Part I Axiomatic K-theory
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1 The Axiomatic Theory
1.1 E-C*-algebras
1.2 The Axioms
1.3 Some Elementary Results
1.4 Tensor Products
1.5 The Class ϒ
1.6 The Class ϒ1
2 Locally Compact Spaces
2.1 Tietze’s Theorem
2.2 Alexandroff Compactification
2.3 Topological Sums of Locally Compact Spaces
2.4 Homotopy
3 Some Selected Locally Spaces
3.1 Balls
3.2 Euclidean Spaces and Spheres
3.3 Some Morphisms
3.4 Some Non-orientable Compact Spaces
3.5 Pasting Locally Compact Spaces
4 Some Supplementary Results
4.1 Full E-C*-algebras
4.2 Continuity and Stability
Part II Projective K-theory
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5 Some Notation and the Axiom
6 The Functor K0
6.1 K0 for CE
6.2 K0 for ME
6.3 Stability of K0
7 The Functor K1
7.1 Definition of K1
7.2 The Index Map
7.3 K1( F) ≈ K0 (SF)
8 Bott Periodicity
8.1 The Bott Map
8.2 Higman’s Linearization Trick
8.3 The Periodicity
9 Variation of the Parameters
9.1 Changing E
9.2 Changing f
Back Matter
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Author(s)
Corneliu Constantinescu is emeritus professor of the Swiss Federal Institute of Technology Zürich. He worked in the Theory of Riemann surfaces, Axiomatic Potential Theory, Spaces of Measures, and C*-algebras and he published books in all these fields.
Description
The book consists of two parts. Part I is an axiomatic frame for the K-theory for C*-algebras. Some central results of this theory are heaved to the status of axioms and the other results are then derived from these axioms. In Part II the author constructs an example for this axiomatic theory which generalizes the classical theory for C*-algebras.
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