[PDF] L2 Invariants eBook

Author : Wolfgang Lück
Publisher : Springer Science & Business Media
Page : 604 pages
File Size : 11,77 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662046873

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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 L2-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. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Author : Holger Kammeyer
Publisher : Springer Nature
Page : 190 pages
File Size : 41,63 MB
Release : 2019-10-29
Category : Mathematics
ISBN : 303028297X

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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.

Author : Wolfgang Lück
Publisher : Springer
Page : 595 pages
File Size : 50,23 MB
Release : 2002-08-06
Category : Mathematics
ISBN : 9783540435662

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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 L2-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. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Author : Zhenghan Wang
Publisher : World Scientific
Page : 466 pages
File Size : 42,85 MB
Release : 2008
Category : Mathematics
ISBN : 9812819118

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This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.The volume includes works on picture (2+1)-TQFTs and their applications to quantum computing, Berry phase and YangOCoBaxterization of the braid relation, finite type invariant of knots, categorification and Khovanov homology, GromovOCoWitten type invariants, twisted Alexander polynomials, Faddeev knots, generalized Ricci flow, CalabiOCoYau problems for CR manifolds, Milnor''s conjecture on volume of simplexes, Heegaard genera of 3-manifolds, and the (A, B)-slice problem. It also includes five unpublished papers of Xiao-Song Lin and various speeches related to the memorial conference

Author : Mo-Lin Ge
Publisher : World Scientific
Page : 542 pages
File Size : 31,95 MB
Release : 2006
Category : Mathematics
ISBN : 9812703772

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This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.

Author : Weiping Zhang
Publisher : World Scientific
Page : 542 pages
File Size : 20,48 MB
Release : 2006-12-11
Category : Mathematics
ISBN : 9814476587

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This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.

Author : Pierre-Emmanuel Caprace
Publisher : Cambridge University Press
Page : 367 pages
File Size : 39,14 MB
Release : 2018-02-08
Category : Mathematics
ISBN : 1108413129

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A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

Author : Martin R. Bridson
Publisher : Cambridge University Press
Page : 331 pages
File Size : 42,61 MB
Release : 2009-10-29
Category : Mathematics
ISBN : 052175724X

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An extended tour through a selection of the most important trends in modern geometric group theory.

Author : Ivan Veselic
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 29,86 MB
Release : 2008-01-02
Category : Mathematics
ISBN : 3540726896

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This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.