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Home / Books / Published Books / Axiomatic K-theory for C*-algebras

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

To purchase hard copies of this book, please email:
book@sciencepublishinggroup.com

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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 C_E

6.2 K₀ for M_E

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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