Topological and Bivariant K-Theory (Oberwolfach Seminars, 36) 2007th Edition by Joachim Cuntz (PDF)

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Ebook Info

  • Published: 2007
  • Number of pages: 274 pages
  • Format: PDF
  • File Size: 1.95 MB
  • Authors: Joachim Cuntz

Description

Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

User’s Reviews

Editorial Reviews: From the Back Cover Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory.We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you know this subject, you would never miss this book. If you do not understand what the book title says, I can not explain anything more.

Keywords

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