Download or read book Mapping Class Subgroups of Outer Automorphism Groups of Free Groups written by Matthew Eugene Horak and published by . This book was released on 2003 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Download or read book Geometric Properties of Outer Automorphism Groups of Free Groups written by Samuel Joseph Taylor and published by . This book was released on 2014 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis examines geometric aspects of the outer automorphism group of a finitely generate free group. Using recent advances made in understanding mapping class groups as our primary motivation, we refine methods to understand the structure of Out(F_n) via its action on free factors of F_n. Our investigation has a number of applications: First, we give a natural notion of projection between free factors, extending a construction of Bestvina-Feighn. Second, we provide a new method to produce fully irreducible automorphisms of F_n using combinations of automorphism supported on free factors. Finally, we use these results to give a general construction of quasi-isometric embeddings from right-angled Artin groups into Out(F_n).
Download or read book Arithmetic Groups and Their Generalizations written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2008 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
Download or read book Arboreal Group Theory written by Roger C. Alperin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the week of September 13, 1988 the Mathematical Sciences Research Institute hosted a four day workshop on Arboreal Group Theory. This volume is the product of that meeting. The program centered on the topic of the theory of groups acting on trees and the various applications to hyperbolic geometry. Topics include the theory of length functions, structure of groups acting freely on trees, spaces of hyperbolic structures and their compactifications, and moduli for tree actions.
Download or read book Subgroup Decomposition in Out Fn written by Michael Handel and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work the authors develop a decomposition theory for subgroups of Out(Fn) which generalizes the decomposition theory for individual elements of Out(Fn) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.
Download or read book Representation Theory written by Zongzhu Lin and published by American Mathematical Soc.. This book was released on 2009-01-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided
Download or read book Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces written by F. Dahmani and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Extended Abstracts Fall 2012 written by Juan González-Meneses and published by Springer. This book was released on 2014-07-24 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features seventeen extended conference abstracts corresponding to selected talks given by participants at the CRM research program “Automorphisms of Free Groups: Algorithms, Geometry and Dynamics”, which took place at the Centre de Recerca Matemàtica in Barcelona in fall 2012. Most of them are short articles giving preliminary presentations of new results not yet published in regular research journals. The articles are the result from a direct collaboration among active researchers in the area after working in a dynamic and productive atmosphere. The book is intended for established researchers in the area of Group Theory, as well as for PhD and postdoc students who wish to learn more about the latest advances in this active area of research.
Download or read book Surface realizable Finite Groups of Outer Automorphisms of Finitely generated Free Groups written by Christopher Thomas and published by . This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A homeomorphism from a punctured surface to itself induces an outer automorphism of the free fundamental group of the surface, an outer automorphism which can be called surface-realizable. This paper provides necessary and sufficient conditions for a finite abelian group of outer automorphisms of a finitely-generated free group to be surface-realizable. Furthermore, n.a.s.c. are given for any finite group of such outer automorphisms to be realized by orientation-preserving homeomorphisms of an orientable surface. These properties are identified by examining those finite subgroups of automorphisms which are mapped into the group of outer automorphisms by the usual projection, and making sure that the non-trivial automorphisms fix either a trivial or cyclic subgroup of the free group. Examples are given to show the difficulties in applying this method to non-abelian cases.
Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.
Download or read book Mapping Class Groups and Moduli Spaces of Riemann Surfaces written by Carl-Friedrich Bödigheimer and published by American Mathematical Soc.. This book was released on 1993 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.
Download or read book Some Solvable Subgroups of the Outer Automorphism Group of a Finite Group written by Nguyen Cao Dam and published by . This book was released on 1972 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book SIMILITUDES OF SURFACE MAPPING CLASS GROUPS AND REDUCIBLE OUTER AUTOMORPHISMS OF FREE GROUPS written by KENNETH MICHAEL BOUCHER and published by . This book was released on 1990 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: defined.
Download or read book Lectures on Geometry written by Nicholas Michael John Woodhouse and published by Oxford University Press. This book was released on 2017 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a series of chapters by leading researchers and practitioners on community engagement approaches in the field of counterterrorism and counterinsurgency. It presents existing and emerging community engagement models in various parts of the world which could serve as effective models for governments keen to work with community leaders to manage and reduce the terrorist threat. The book emphasizes the strength of communities as central to government approaches in countering violent extremism.
Download or read book Infinite Groups Geometric Combinatorial and Dynamical Aspects written by Laurent Bartholdi and published by Springer Science & Business Media. This book was released on 2006-03-28 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.
Download or read book Mapping Tori of Outer Automorphisms of Free Groups written by Zhifeng Wang and published by . This book was released on 2002 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
