L2 Invariants Theory And Applications To Geometry And K Theory
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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.
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 : 2013-03-09
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 2013-03-09 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. It is particularly these interactions with different fields that make L2-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.
L2 Invariants
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Author : Wolfgang Luck
language : en
Publisher:
Release Date : 2014-01-15
L2 Invariants written by Wolfgang Luck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Computers Rigidity And Moduli
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Author : Shmuel Weinberger
language : en
Publisher: Princeton University Press
Release Date : 2020-12-08
Computers Rigidity And Moduli written by Shmuel Weinberger 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 2020-12-08 with Mathematics categories.
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
A Course On Surgery Theory
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Author : Stanley Chang
language : en
Publisher: Princeton University Press
Release Date : 2021-01-26
A Course On Surgery Theory written by Stanley Chang 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 2021-01-26 with Mathematics categories.
An advanced treatment of surgery theory for graduate students and researchers Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. A Course on Surgery Theory offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest. Of significant use to high-dimensional topologists and researchers in noncommutative geometry and algebraic K-theory, A Course on Surgery Theory serves as an important resource for the mathematics community.
High Dimensional Manifold Topology
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Author : R. T. Farrell
language : en
Publisher: World Scientific
Release Date : 2003
High Dimensional Manifold Topology written by R. T. Farrell and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book covers topics such as manifolds with positive scalar curvature, pseudo-isotopy spectrum and controlled theory, and reduction of the Novikov and Borel conjectures for aspherical complexes to aspherical manifolds.
Exercises In Cellular Automata And Groups
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Nature
Release Date : 2023-11-01
Exercises In Cellular Automata And Groups written by Tullio Ceccherini-Silberstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-01 with Mathematics categories.
This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk
Spectral Analysis On Graph Like Spaces
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Author : Olaf Post
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-06
Spectral Analysis On Graph Like Spaces written by Olaf Post 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 2012-01-06 with Mathematics categories.
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
Noncommutative Localization In Algebra And Topology
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Author : Andrew Ranicki
language : en
Publisher: Cambridge University Press
Release Date : 2006-02-09
Noncommutative Localization In Algebra And Topology written by Andrew Ranicki 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 2006-02-09 with Mathematics categories.
Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. Originally conceived by algebraists (notably P. M. Cohn), it is now an important tool not only in pure algebra but also in the topology of non-simply-connected spaces, algebraic geometry and noncommutative geometry. This volume consists of 9 articles on noncommutative localization in algebra and topology by J. A. Beachy, P. M. Cohn, W. G. Dwyer, P. A. Linnell, A. Neeman, A. A. Ranicki, H. Reich, D. Sheiham and Z. Skoda. The articles include basic definitions, surveys, historical background and applications, as well as presenting new results. The book is an introduction to the subject, an account of the state of the art, and also provides many references for further material. It is suitable for graduate students and more advanced researchers in both algebra and topology.