Lecture Notes in Mathematics

Introduction to ℓ²-invariants

Authors: Kammeyer, Holger

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  • An up-to-date and user-friendly introduction to the rapidly developing field of l ²-invariants
  • Proceeds quickly to the research level after thoroughly covering all the basics
  • Contains many motivating examples, illustrations, and exercises
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eBook $39.99
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  • ISBN 978-3-030-28297-4
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Softcover $49.99
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  • ISBN 978-3-030-28296-7
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About this book

This book introduces the reader to the most important concepts and problems in the field of ℓ²-invariants. After some foundational material on group von Neumann algebras, ℓ²-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of ℓ²-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of ℓ²-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with ℓ²-torsion, twisted variants and the conjectures relating them to torsion growth in homology. The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.

About the authors

Holger Kammeyer studied Mathematics at Göttingen and Berkeley. After a postdoc position in Bonn he is now based at Karlsruhe Institute of Technology. His research interests range around algebraic topology and group theory. The application of ℓ ²-invariants forms a recurrent theme in his work. He has given introductory courses on the matter on various occasions.

Reviews

“This is an excellent introductory book, to be recommended to readers looking for an introduction to the field, as well as those that want to have an overview of recent developments.” (Joan Porti, Mathematical Reviews, September, 2020)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-030-28297-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-030-28296-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to ℓ²-invariants
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2247
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-28297-4
DOI
10.1007/978-3-030-28297-4
Softcover ISBN
978-3-030-28296-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 183
Number of Illustrations
37 b/w illustrations
Topics