analysis and geometry on groups cambridge tracts in mathematics

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Analysis And Geometry On Groups

Author : Nicholas T. Varopoulos
ISBN : 0521088011
Genre : Mathematics
File Size : 52. 21 MB
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The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.

Geometric Group Theory

Author : Cornelia Druţu
ISBN : 9781470411046
Genre : Geometric group theory
File Size : 46. 41 MB
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The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

Geometric Group Theory Down Under

Author : John Cossey
ISBN : 3110163667
Genre : Mathematics
File Size : 81. 1 MB
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Seventeen contributions from the July 1996 conference present current research in the theory of algebraic groups, the theory of automatic and hyperbolic groups, convergence groups, distortion of subgroups, Artin groups and braid groups, amenable groups, combinatorial approaches to conformal structure, algebraic and geometric automorphism groups, and geometric invariants of groups. Some of the specific topics are the topology of polynomial varieties, the intersection of flat subsets of a braid group, embedding free amalgams of discrete groups in non-discrete topological groups, automatic structures on central extensions, and whitehead graphs on handlebodies. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Topics In Geometric Group Theory

Author : Pierre de la Harpe
ISBN : 0226317196
Genre : Mathematics
File Size : 50. 3 MB
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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.

The Cube A Window To Convex And Discrete Geometry

Author : Chuanming Zong
ISBN : 9781139448642
Genre : Mathematics
File Size : 42. 47 MB
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This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. However, our knowledge about them is still quite limited and many basic problems remain unsolved. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular the author demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture.

Handbook Of Geometric Topology

Author : R.B. Sher
ISBN : 0080532853
Genre : Mathematics
File Size : 51. 85 MB
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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.

Perspectives In Analysis Geometry And Topology

Author : Ilia Itenberg
ISBN : 9780817682774
Genre : Mathematics
File Size : 67. 51 MB
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The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Random Walks On Infinite Graphs And Groups

Author : Wolfgang Woess
ISBN : 0521552923
Genre : Mathematics
File Size : 73. 82 MB
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The main theme of this book is the interplay between random walks and discrete structure theory.

Graph Directed Markov Systems

Author : R. Daniel Mauldin
ISBN : 0521825385
Genre : Mathematics
File Size : 82. 13 MB
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Monograph on Graph Directed Markov Systems with backgound and research level material.

Group Cohomology And Algebraic Cycles

Author : Burt Totaro
ISBN : 9781107015777
Genre : Mathematics
File Size : 48. 88 MB
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This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

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