L2-invariants: theory and applications to geometry and K-theory
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In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L 2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K -Theory, differential geometry, non-commutative geometry and spectral theory. It is particularly these interactions with different fields that make L 2-invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments. It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material.
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L2-invariants: theory and applications to geometry and K-theory, Wolfgang Luck
- Language
- Released
- 2002
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- Title
- L2-invariants: theory and applications to geometry and K-theory
- Language
- English
- Authors
- Wolfgang Luck
- Publisher
- Springer
- Released
- 2002
- ISBN10
- 3540435662
- ISBN13
- 9783540435662
- Series
- Ergebnisse der Mathematik und ihrer Grenzgebiete
- Category
- Mathematics
- Description
- In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L 2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K -Theory, differential geometry, non-commutative geometry and spectral theory. It is particularly these interactions with different fields that make L 2-invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments. It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material.