Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems
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Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems
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Author : Denis V. Osin
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems written by Denis V. Osin 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 2006 with Mathematics categories.
In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.
Hyperbolically Embedded Subgroups And Rotating Families In Groups Acting On Hyperbolic Spaces
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Author : F. Dahmani
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-01-18
Hyperbolically Embedded Subgroups And Rotating Families In Groups Acting On Hyperbolic Spaces written by F. Dahmani 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 2017-01-18 with Mathematics categories.
he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.
Geometric Group Theory
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Author : Cornelia Druţu
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-28
Geometric Group Theory written by Cornelia Druţu 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 2018-03-28 with Mathematics categories.
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.
Geometry Topology And Dynamics In Negative Curvature
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Author : C. S. Aravinda
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-21
Geometry Topology And Dynamics In Negative Curvature written by C. S. Aravinda 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 2016-01-21 with Mathematics categories.
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
From Riches To Raags 3 Manifolds Right Angled Artin Groups And Cubical Geometry
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Author : Daniel T. Wise
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
From Riches To Raags 3 Manifolds Right Angled Artin Groups And Cubical Geometry written by Daniel T. Wise 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 2012 with Mathematics categories.
Wise describes a stream of geometric group theory connecting many of the classically considered groups arising in combinatorial group theory with right-angled Artin groups. He writes for new or seasoned researchers who have completed at least an introductory course of geometric groups theory or even just hyperbolic groups, but says some comfort with graphs of groups would be helpful. His topics include non-positively curved cube complexes, virtual specialness of malnormal amalgams, finiteness properties of the dual cube complex, walls in cubical small-cancellation theory, and hyperbolicity and quasiconvexity detection. Color drawings illustrate. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com).
Fields Of Logic And Computation Iii
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Author : Andreas Blass
language : en
Publisher: Springer Nature
Release Date : 2020-05-22
Fields Of Logic And Computation Iii written by Andreas Blass and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-22 with Computers categories.
This Festschrift is published in honor of Yuri Gurevich’s 80th birthday. An associated conference, YuriFest 2020, was planned for May 18–20 in Fontainebleau, France, in combination with the 39th Journées sur les Arithmétiques Faibles also celebrating Yuri’s 80th birthday. Because of the coronavirus situation, the conference had to be postponed, but this Festschrift is being published as originally planned. It addresses a very wide variety of topics, but by no means all of the fields of logic and computation in which Yuri has made important progress.
The Structure Of Groups With A Quasiconvex Hierarchy
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Author : Daniel T. Wise
language : en
Publisher: Princeton University Press
Release Date : 2021-05-04
The Structure Of Groups With A Quasiconvex Hierarchy written by Daniel T. Wise 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 2021-05-04 with Mathematics categories.
This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory that generalizes ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams. The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology.
Beyond Hyperbolicity
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Author : Mark Hagen
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-11
Beyond Hyperbolicity written by Mark Hagen 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 2019-07-11 with Mathematics categories.
Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.
Topological And Asymptotic Aspects Of Group Theory
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Author : R. I. Grigorchuk
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Topological And Asymptotic Aspects Of Group Theory written by R. I. Grigorchuk 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 2006 with Mathematics categories.
The articles in this volume are based on the talks given at two special sessions at the AMS Sectional meetings held in 2004. The articles cover various topological and asymptotic aspects of group theory, such as hyperbolic and relatively hyperbolic groups, asymptotic cones, Thompson's group, Nielsen fixed point theory, homology, groups acting on trees, groups generated by finite automata, iterated monodromy groups, random walks on finitely generated groups, heat kernels, and currents on free groups.
A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem Heuristics And Rigorous Verification On A Model
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Author : Amadeu Delshams
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem Heuristics And Rigorous Verification On A Model written by Amadeu Delshams 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 2006 with Mathematics categories.
Beginning by introducing a geometric mechanism for diffusion in a priori unstable nearly integrable dynamical systems. This book is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and tori of lower dimension. It argues that these objects created by resonances can be incorporated in transition chains taking the place of the destroyed primary KAM tori.The authors establish rigorously the existence of this mechanism in a simplemodel that has been studied before. The main technique is to develop a toolkit to study, in a unified way, tori of different topologies and their invariant manifolds, their intersections as well as shadowing properties of these bi-asymptotic orbits. This toolkit is based on extending and unifyingstandard techniques. A new tool used here is the scattering map of normally hyperbolic invariant manifolds.The model considered is a one-parameter family, which for $\varepsilon = 0$ is an integrable system. We give a small number of explicit conditions the jet of order $3$ of the family that, if verified imply diffusion. The conditions are just that some explicitely constructed functionals do not vanish identically or have non-degenerate critical points, etc.An attractive feature of themechanism is that the transition chains are shorter in the places where the heuristic intuition and numerical experimentation suggests that the diffusion is strongest.