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 : 45. 86 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 : 21. 10 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 : 58. 77 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 : 59. 52 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.

Random Walks On Infinite Graphs And Groups

Author : Wolfgang Woess
ISBN : 0521552923
Genre : Mathematics
File Size : 60. 32 MB
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The main theme of this book is the interplay between random walks and discrete structure theory.

The Geometry Of Discrete Groups

Author : Alan F. Beardon
ISBN : 9781461211464
Genre : Mathematics
File Size : 47. 26 MB
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This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now well-known (but virtually unobtainable) Fenchel-Nielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geo metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana tions are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right.

Jordan Structures In Geometry And Analysis

Author : Cho-Ho Chu
ISBN : 9781139505437
Genre : Mathematics
File Size : 79. 89 MB
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Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.

Graph Directed Markov Systems

Author : R. Daniel Mauldin
ISBN : 0521825385
Genre : Mathematics
File Size : 78. 41 MB
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Monograph on Graph Directed Markov Systems with backgound and research level material.

Automorphic Forms On Sl2 R

Author : Armand Borel
ISBN : 0521580498
Genre : Mathematics
File Size : 34. 80 MB
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An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

Floer Homology Groups In Yang Mills Theory

Author : S. K. Donaldson
ISBN : 1139432605
Genre : Mathematics
File Size : 43. 78 MB
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The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.

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