L2 Invariants Theory And Applications To Geometry And K Theory
Download L2 Invariants Theory And Applications To Geometry And K Theory full books in PDF, epub, and Kindle. Read online free L2 Invariants Theory And Applications To Geometry And K Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Wolfgang Lück |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 604 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662046873 |
Download L2-Invariants: Theory and Applications to Geometry and K-Theory Book in PDF, Epub and Kindle
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 | : Wolfgang Luck |
| Publisher | : |
| Total Pages | : 612 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662046883 |
Download L2-Invariants Book in PDF, Epub and Kindle
| Author | : Wolfgang Lück |
| Publisher | : Springer |
| Total Pages | : 595 |
| Release | : 2002-08-06 |
| Genre | : Mathematics |
| ISBN | : 9783540435662 |
Download L2-Invariants: Theory and Applications to Geometry and K-Theory Book in PDF, Epub and Kindle
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 |
| Total Pages | : 190 |
| Release | : 2019-10-29 |
| Genre | : Mathematics |
| ISBN | : 303028297X |
Download Introduction to l2-invariants Book in PDF, Epub and Kindle
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 | : Martin R. Bridson |
| Publisher | : Cambridge University Press |
| Total Pages | : 331 |
| Release | : 2009-10-29 |
| Genre | : Mathematics |
| ISBN | : 052175724X |
Download Geometric and Cohomological Methods in Group Theory Book in PDF, Epub and Kindle
An extended tour through a selection of the most important trends in modern geometric group theory.
| Author | : Guido Mislin |
| Publisher | : Birkhäuser |
| Total Pages | : 138 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034880898 |
Download Proper Group Actions and the Baum-Connes Conjecture Book in PDF, Epub and Kindle
A concise introduction to the techniques used to prove the Baum-Connes conjecture. The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area, leading to current research problems.
| Author | : Nigel Higson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 212 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9780821838464 |
Download Surveys in Noncommutative Geometry Book in PDF, Epub and Kindle
In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ``ordinary'' geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the ``residue index theorem'' of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
| Author | : Haynes Miller |
| Publisher | : CRC Press |
| Total Pages | : 982 |
| Release | : 2020-01-23 |
| Genre | : Mathematics |
| ISBN | : 1351251619 |
Download Handbook of Homotopy Theory Book in PDF, Epub and Kindle
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
| Author | : Giuseppe Dito |
| Publisher | : World Scientific |
| Total Pages | : 537 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 981442501X |
Download Noncommutative Geometry and Physics 3 Book in PDF, Epub and Kindle
Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.
| Author | : Dan Burghelea |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2008-03-18 |
| Genre | : Mathematics |
| ISBN | : 3764386045 |
Download C*-algebras and Elliptic Theory II Book in PDF, Epub and Kindle
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
