L2 Invariants
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L2 Invariants Theory And Applications To Geometry And K Theory
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Author : Wolfgang Lück
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-08-06
L2 Invariants Theory And Applications To Geometry And K Theory written by Wolfgang Lück and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-06 with Mathematics categories.
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.
Introduction To L2 Invariants
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Author : Holger Kammeyer
language : en
Publisher: Springer Nature
Release Date : 2019-10-29
Introduction To L2 Invariants written by Holger Kammeyer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Mathematics categories.
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.
Geometric Analysis And Lie Theory In Mathematics And Physics
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Author : Alan L. Carey
language : en
Publisher: Cambridge University Press
Release Date : 1998
Geometric Analysis And Lie Theory In Mathematics And Physics written by Alan L. Carey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Graduate lectures on the interface between mathematics and physics.
Topology And Physics
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Author : Zhenghan Wang
language : en
Publisher: World Scientific
Release Date : 2008
Topology And Physics written by Zhenghan Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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
Geometry And Topology Of Aspherical Manifolds
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Author : Luca F. Di Cerbo
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-31
Geometry And Topology Of Aspherical Manifolds written by Luca F. Di Cerbo and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-31 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Singer–Hopf Conjecture in Geometry and Topology, held from March 18–19, 2023, at Georgia Institute of Technology, Atlanta, Georgia. It presents a multidisciplinary point of view on the Singer conjecture, the Hopf conjecture, the study on normalized Betti numbers, and several other intriguing questions on the fundamental group and cohomology of aspherical manifolds. This volume highlights many interesting research directions in the study of aspherical manifolds and covers a large collection of problems and conjectures about $L^2$-invariants of aspherical manifolds. It provides a snapshot of contemporary research in mathematics at the interface of geometry and topology, as well as algebraic geometry. The problems are presented from several distinct points of view, and the articles in this volume suggest possible generalizations and bridge a gap with closely related problems in differential geometry, complex algebraic geometry, and geometric topology. The volume can play a role in focusing the attention of the mathematical community on these fascinating problems which continue to resist the siege of geometers and topologists. It is our hope that this volume will become a valuable resource for early career mathematicians interested in these deep and important questions.
Handbook Of Geometric Topology
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Author : R.B. Sher
language : en
Publisher: Elsevier
Release Date : 2001-12-20
Handbook Of Geometric Topology written by R.B. Sher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-20 with Mathematics categories.
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Existence And Regularity Properties Of The Integrated Density Of States Of Random Schr Dinger Operators
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Author : Ivan Veselic
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-02
Existence And Regularity Properties Of The Integrated Density Of States Of Random Schr Dinger Operators written by Ivan Veselic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-02 with Mathematics categories.
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.
Geometric And Cohomological Methods In Group Theory
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Author : Martin R. Bridson
language : en
Publisher: Cambridge University Press
Release Date : 2009-10-29
Geometric And Cohomological Methods In Group Theory written by Martin R. Bridson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-29 with Mathematics categories.
An extended tour through a selection of the most important trends in modern geometric group theory.
Lectures On K Hler Groups
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Author : Pierre Py
language : en
Publisher: Princeton University Press
Release Date : 2025-03-25
Lectures On K Hler Groups written by Pierre Py and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
An introduction to the state of the art in the study of Kähler groups This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact Kähler manifolds, known as Kähler groups. Approaching the subject from the perspective of a geometric group theorist, Pierre Py equips readers with the necessary background in both geometric group theory and Kähler geometry, covering topics such as the actions of Kähler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact Kähler manifolds, and the topology of level sets of pluriharmonic functions. Presenting the most important results from the past three decades, the book provides graduate students and researchers with detailed original proofs of several central theorems, including Gromov and Schoen’s description of Kähler group actions on trees; the study of solvable quotients of Kähler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran’s work characterizing covering spaces of compact Kähler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field. Lectures on Kähler Groups also gives, in eight appendixes, detailed introductions to such topics as the study of ends of groups and spaces, groups acting on trees and Hilbert spaces, potential theory, and L2 cohomology on Riemannian manifolds.
Tel Aviv Topology Conference Rothenberg Festschrift
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Author : Melvin Rothenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Tel Aviv Topology Conference Rothenberg Festschrift written by Melvin Rothenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents the proceedings of the Tel Aviv International Topology Conference held during the Special Topology Program at Tel Aviv University. The book is dedicated to Professor Mel Rothenberg on the occasion of his 65th birthday. His contributions to topology are well known-from the early work on triangulations to numerous papers on transformation groups and on geometric and analytic aspects of torsion theory. Current research related to those contributions are reported in this book. Coverage is included on the following topics: vanishing theorems for the Dirac operator, the theory of Reidemeister torsion (including infinite dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of group actions, Lusternik-Schnirelman theory for closed 1-forms, finite type invariants of links and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and more.