Index Theory Coarse Geometry And Topology Of Manifolds
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Index Theory Coarse Geometry And Topology Of Manifolds
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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Index Theory Coarse Geometry And Topology Of Manifolds written by John Roe 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 1996 with Mathematics categories.
Lecture notes from the conference held Aug. 1995 in Boulder, Colo.
Coarse Cohomology And Index Theory On Complete Riemannian Manifolds
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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Coarse Cohomology And Index Theory On Complete Riemannian Manifolds written by John Roe 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 1993 with Mathematics categories.
"July 1993, volume 104, number 497 (fourth of 6 numbers)."
Coarse Cohomology And Index Theory On Complete Riemannian Manifolds
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Author : Both Professors of Maths John Roe
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-08-31
Coarse Cohomology And Index Theory On Complete Riemannian Manifolds written by Both Professors of Maths John Roe and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with MATHEMATICS categories.
Coarse geometry'' is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which look the same from a great distance'' are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct higher indices'' for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the $K$-theory of a certain operator algebra naturally associated to the coarse structure, and this $K$-theory then pairs with the coarse cohomology. The higher indices can be calculated in topological terms thanks to the work of Connes and Moscovici. They can also be interpreted in terms of the $K$-homology of an ideal boundary naturally associated to the coarse structure. Applications to geometry are given, and the book concludes with a discussion of the coarse analog of the Novikov conjecture.
Lectures On Coarse Geometry
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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date :
Lectures On Coarse Geometry written by John Roe 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 with Mathematics categories.
Coarse geometry is the study of spaces (particularly metric spaces) from a ''large scale'' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famousrigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. Themiddle section of the book reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent ''large scale'' rendition of the crucial properties of negatively curved spaces. The final chapters discuss recent results on asymptotic dimension and uniform embeddings into Hilbert space. John Roe is known for his work on index theory, coarse geometry, and topology. His exposition is clear anddirect, bringing insight to this modern field of mathematics. Students and researchers who wish to learn about contemporary methods of understanding the geometry and topology of manifolds will be well served by reading this book. Also available from the AMS by John Roe is Index Theory, CoarseGeometry, and Topology of Manifolds.
Higher Index Theory
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Author : Rufus Willett
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-02
Higher Index Theory written by Rufus Willett 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 2020-07-02 with Mathematics categories.
A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.
Relative Index Theory Determinants And Torsion For Open Manifolds
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Author : Jrgen Eichhorn
language : en
Publisher: World Scientific
Release Date : 2009
Relative Index Theory Determinants And Torsion For Open Manifolds written by Jrgen Eichhorn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.
Relative Index Theory Determinants And Torsion For Open Manifolds
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language : en
Publisher:
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Relative Index Theory Determinants And Torsion For Open Manifolds written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Generic Coarse Geometry Of Leaves
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Author : Jesús A. Álvarez López
language : en
Publisher: Springer
Release Date : 2018-07-28
Generic Coarse Geometry Of Leaves written by Jesús A. Álvarez López and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-28 with Mathematics categories.
This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants. Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas. When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves. Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry. Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples. The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.
Coarse Geometry Of Topological Groups
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Author : Christian Rosendal
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Coarse Geometry Of Topological Groups written by Christian Rosendal 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 2021-12-16 with Mathematics categories.
Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
Index Theory And Operator Algebras
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Author : Jeffrey Stephen Fox
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
Index Theory And Operator Algebras written by Jeffrey Stephen Fox 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 1993-01-01 with Mathematics categories.
This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on K-Homology and Index Theory, held in August 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple p-adic groups and the geometry of discrete groups are also discussed. Through-out the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on index theory.