Lectures On Coarse Geometry

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Lectures On Coarse Geometry

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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

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 2003 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 book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.

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.

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.

Lectures On Formal And Rigid Geometry

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Author : Siegfried Bosch
language : en
Publisher: Springer
Release Date : 2014-08-22

Lectures On Formal And Rigid Geometry written by Siegfried Bosch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".

A Course In Metric Geometry

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Author : Dmitri Burago
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

A Course In Metric Geometry written by Dmitri Burago 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 2001 with Mathematics categories.

"Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces).

Lectures On The Geometry Of Manifolds

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Author : Liviu I. Nicolaescu
language : en
Publisher: World Scientific
Release Date : 2007

Lectures On The Geometry Of Manifolds written by Liviu I. Nicolaescu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that ?in learning the sciences examples are of more use than precepts?. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a ?global and analytical bias?. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar‚ duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-;Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand H”lder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

Noncommutative Geometry And Physics 3 Proceedings Of The Noncommutative Geometry And Physics 2008 On K Theory And D Branes Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry

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Author : Giuseppe Dito
language : en
Publisher: World Scientific
Release Date : 2013-01-11

Noncommutative Geometry And Physics 3 Proceedings Of The Noncommutative Geometry And Physics 2008 On K Theory And D Branes Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry written by Giuseppe Dito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Mathematics categories.

Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of 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. It is an important topic both for mathematics and physics.

Coarse Geometry And Randomness

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Author : Itai Benjamini
language : en
Publisher: Springer
Release Date : 2013-12-02

Coarse Geometry And Randomness written by Itai Benjamini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-02 with Mathematics categories.

These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ).

Strasbourg Master Class On Geometry

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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2012

Strasbourg Master Class On Geometry written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master classes in 2008 and 2009. The aim of the master classes was to give fifth-year students and Ph.D. students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were taught by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmuller theory, Lie groups, and asymptotic geometry. The text is aimed at graduate students and research mathematicians. It can also be used as a reference book and as a textbook for short courses on geometry.

Topics In Geometric Group Theory

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Author : Pierre de la Harpe
language : en
Publisher: University of Chicago Press
Release Date : 2000-10-15

Topics In Geometric Group Theory written by Pierre de la Harpe and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-15 with Education categories.

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.