Algorithmic And Geometric Topics Around Free Groups And Automorphisms

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Algorithmic and Geometric Topics Around Free Groups and Automorphisms

Javier Aramayona,Volker Diekert,Christopher J. Leininger,Pedro V. Silva,Armin Weiß
Algorithmic and Geometric Topics Around Free Groups and Automorphisms Book PDF

Author : Javier Aramayona,Volker Diekert,Christopher J. Leininger,Pedro V. Silva,Armin Weiß
Publisher : Birkhäuser
Page : 149 pages
File Size : 49,7 Mb
Release : 2017-11-29
Category : Mathematics
ISBN : 9783319609409

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Algorithmic and Geometric Topics Around Free Groups and Automorphisms by Javier Aramayona,Volker Diekert,Christopher J. Leininger,Pedro V. Silva,Armin Weiß Pdf

This volume presents the lecture notes from the authors’ three summer courses offered during the program “Automorphisms of Free Groups: Geometry, Topology, and Dynamics,” held at the Centre de Recerca Matemàtica (CRM) in Bellaterra, Spain. The first two chapters present the basic tools needed, from formal language theory (regular and context-free languages, automata, rewriting systems, transducers, etc) and emphasize their connections to group theory, mostly relating to free and virtually-free groups. The material covered is sufficient to present full proofs of many of the existing interesting characterizations of virtually-free groups. In turn, the last chapter comprehensively describes Bonahon’s construction of Thurston’s compactification of Teichmüller space in terms of geodesic currents on surfaces. It also includes several intriguing extensions of the notion of geodesic current to various other, more general settings.

Mirzakhani’s Curve Counting and Geodesic Currents

Viveka Erlandsson,Juan Souto
Mirzakhani s Curve Counting and Geodesic Currents Book PDF

Author : Viveka Erlandsson,Juan Souto
Publisher : Springer Nature
Page : 233 pages
File Size : 48,5 Mb
Release : 2022-09-20
Category : Mathematics
ISBN : 9783031087059

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Mirzakhani’s Curve Counting and Geodesic Currents by Viveka Erlandsson,Juan Souto Pdf

This monograph presents an approachable proof of Mirzakhani’s curve counting theorem, both for simple and non-simple curves. Designed to welcome readers to the area, the presentation builds intuition with elementary examples before progressing to rigorous proofs. This approach illuminates new and established results alike, and produces versatile tools for studying the geometry of hyperbolic surfaces, Teichmüller theory, and mapping class groups. Beginning with the preliminaries of curves and arcs on surfaces, the authors go on to present the theory of geodesic currents in detail. Highlights include a treatment of cusped surfaces and surfaces with boundary, along with a comprehensive discussion of the action of the mapping class group on the space of geodesic currents. A user-friendly account of train tracks follows, providing the foundation for radallas, an immersed variation. From here, the authors apply these tools to great effect, offering simplified proofs of existing results and a new, more general proof of Mirzakhani’s curve counting theorem. Further applications include counting square-tiled surfaces and mapping class group orbits, and investigating random geometric structures. Mirzakhani’s Curve Counting and Geodesic Currents introduces readers to powerful counting techniques for the study of surfaces. Ideal for graduate students and researchers new to the area, the pedagogical approach, conversational style, and illuminating illustrations bring this exciting field to life. Exercises offer opportunities to engage with the material throughout. Basic familiarity with 2-dimensional topology and hyperbolic geometry, measured laminations, and the mapping class group is assumed.

Extended Abstracts Fall 2012

Juan González-Meneses,Martin Lustig,Enric Ventura
Extended Abstracts Fall 2012 Book PDF

Author : Juan González-Meneses,Martin Lustig,Enric Ventura
Publisher : Springer
Page : 94 pages
File Size : 42,7 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783319054889

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Extended Abstracts Fall 2012 by Juan González-Meneses,Martin Lustig,Enric Ventura Pdf

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.

Combinatorial and Geometric Group Theory

Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Combinatorial and Geometric Group Theory Book PDF

Author : Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 53,9 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783764399115

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Combinatorial and Geometric Group Theory by Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura Pdf

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Office Hours with a Geometric Group Theorist

Matt Clay,Dan Margalit
Office Hours with a Geometric Group Theorist Book PDF

Author : Matt Clay,Dan Margalit
Publisher : Princeton University Press
Page : 456 pages
File Size : 49,8 Mb
Release : 2017-07-11
Category : Mathematics
ISBN : 9780691158662

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Office Hours with a Geometric Group Theorist by Matt Clay,Dan Margalit Pdf

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Office Hours with a Geometric Group Theorist

Matt Clay,Dan Margalit
Office Hours with a Geometric Group Theorist Book PDF

Author : Matt Clay,Dan Margalit
Publisher : Princeton University Press
Page : 456 pages
File Size : 52,7 Mb
Release : 2017-07-11
Category : Mathematics
ISBN : 9781400885398

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Office Hours with a Geometric Group Theorist by Matt Clay,Dan Margalit Pdf

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Groups, Languages and Geometry

Robert H. Gilman
Groups Languages and Geometry Book PDF

Author : Robert H. Gilman
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 52,8 Mb
Release : 1999
Category : Formal languages
ISBN : 9780821810538

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Groups, Languages and Geometry by Robert H. Gilman Pdf

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). The conference was devoted to computational aspects of geometric group theory, a relatively young area of research which has grown out of an influx of ideas from topology and computer science into combinatorial group theory. The book reflects recent progress in this interesting new field. Included are articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems. There is also a survey of open questions in combinatorial group theory. The volume will interest group theorists, topologists, and experts in automata and language theory.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Gebhard Böckle,Wolfram Decker,Gunter Malle
Algorithmic and Experimental Methods in Algebra Geometry and Number Theory Book PDF

Author : Gebhard Böckle,Wolfram Decker,Gunter Malle
Publisher : Springer
Page : 753 pages
File Size : 40,9 Mb
Release : 2018-03-22
Category : Mathematics
ISBN : 9783319705668

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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by Gebhard Böckle,Wolfram Decker,Gunter Malle Pdf

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Combinatorial Methods

Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu
Combinatorial Methods Book PDF

Author : Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 40,5 Mb
Release : 2012-11-12
Category : Mathematics
ISBN : 9780387217246

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Combinatorial Methods by Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu Pdf

The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.

Combinatorial and Geometric Group Theory

Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain
Combinatorial and Geometric Group Theory Book PDF

Author : Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 41,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828229

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Combinatorial and Geometric Group Theory by Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain Pdf

This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

Geometry of Defining Relations in Groups

A.Yu. Ol'shanskii
Geometry of Defining Relations in Groups Book PDF

Author : A.Yu. Ol'shanskii
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 50,9 Mb
Release : 1991-10-31
Category : Mathematics
ISBN : 0792313941

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Geometry of Defining Relations in Groups by A.Yu. Ol'shanskii Pdf

The main feature of this book is a systematic application of elementary geometric and topological techniques for solving problems that arise naturally in algebra. After an account of preliminary material, there is a discussion of a geometrically intuitive interpretation of the derivation of consequences of defining relations of groups. A study is made of planar and certain other two-dimensional maps connected with well-known problems in general group theory, such as the problems of Burnside and O. Yu. Schmidt. The method of cancellation diagrams developed here is applied to these and to a series of other problems. This monograph is addressed to research workers and students in universities, and may be used as a basis for a series of specialized lectures or seminars.

Combinatorial and Geometric Group Theory

Sean Cleary
Combinatorial and Geometric Group Theory Book PDF

Author : Sean Cleary
Publisher : American Mathematical Soc.
Page : 292 pages
File Size : 41,6 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0821856324

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Combinatorial and Geometric Group Theory by Sean Cleary Pdf

This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

Geometric Group Theory

Goulnara N. Arzhantseva,Laurent Bartholdi,Jose Burillo,Enric Ventura
Geometric Group Theory Book PDF

Author : Goulnara N. Arzhantseva,Laurent Bartholdi,Jose Burillo,Enric Ventura
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 49,5 Mb
Release : 2007-09-24
Category : Mathematics
ISBN : 9783764384128

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Geometric Group Theory by Goulnara N. Arzhantseva,Laurent Bartholdi,Jose Burillo,Enric Ventura Pdf

This volume has its origins in the Barcelona Conference in Group Theory (July 2005) and the conference "Asymptotic and Probabilistic Methods in Geometric Group Theory" held in Geneva (June 2005). Twelve peer-reviewed research articles written by experts in the field present the most recent results in abstract and geometric group theory. In particular there are two articles by A. Juhász.

Algebra VII

D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Algebra VII Book PDF

Author : D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 48,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642580130

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Algebra VII by D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang Pdf

From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

Groups, Languages, and Geometry

Robert H. Gilman
Groups Languages and Geometry Book PDF

Author : Robert H. Gilman
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 50,6 Mb
Release : 1999
Category : Mathematics
ISBN : 0821855867

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Groups, Languages, and Geometry by Robert H. Gilman Pdf

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). The conference was devoted to computational aspects of geometric group theory, a relatively young area of research which has grown out of an influx of ideas from topology and computer science into combinatorial group theory. The book reflects recent progress in this interesting new field. Included are articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems. There is also a survey of open questions in combinatorial group theory. The volume will interest group theorists, topologists, and experts in automata and language theory.