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Author: Lisa Carbone
Publisher: American Mathematical Soc.
ISBN: 0821827219
Category : Mathematics
Languages : en
Pages : 146
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Book Description
This title provides a comprehensive examination of non-uniform lattices on uniform trees. Topics include graphs of groups, tree actions and edge-indexed graphs; $Aut(x)$ and its discrete subgroups; existence of tree lattices; non-uniform coverings of indexed graphs with an arithmetic bridge; non-uniform coverings of indexed graphs with a separating edge; non-uniform coverings of indexed graphs with a ramified loop; eliminating multiple edges; existence of arithmetic bridges. This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Author: Lisa Carbone
Publisher: American Mathematical Soc.
ISBN: 0821827219
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
This title provides a comprehensive examination of non-uniform lattices on uniform trees. Topics include graphs of groups, tree actions and edge-indexed graphs; $Aut(x)$ and its discrete subgroups; existence of tree lattices; non-uniform coverings of indexed graphs with an arithmetic bridge; non-uniform coverings of indexed graphs with a separating edge; non-uniform coverings of indexed graphs with a ramified loop; eliminating multiple edges; existence of arithmetic bridges. This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
Author: Hyman Bass
Publisher: Springer Science & Business Media
ISBN: 146122098X
Category : Mathematics
Languages : en
Pages : 239
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Book Description
This monograph extends this approach to the more general investigation of X-lattices, and these "tree lattices" are the main object of study. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems. Tree Lattices should be a helpful resource to researchers in the field, and may also be used for a graduate course on geometric methods in group theory.
Author: Benson Farb
Publisher: University of Chicago Press
ISBN: 0226237907
Category : Mathematics
Languages : en
Pages : 659
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Book Description
The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1164
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Book Description
Author: Hyman Bass
Publisher: American Mathematical Soc.
ISBN: 0821810871
Category : Mathematics
Languages : en
Pages : 250
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Book Description
This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass, and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.
Author: Eamon Doherty
Publisher: AuthorHouse
ISBN: 1434372316
Category : Computers
Languages : en
Pages : 278
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Book Description
This "Everyone" book attempts to the guide the reader through the more essential steps of understanding the basic principles or elements that constitute the daily work of investigators in fields relating to computing and electrical loss. The chapter's are meant to set a foundation for people who may want to enter the field of investigations, or are at the beginning of a career in the area, or are seasoned investigators looking to delve into more contemporary areas of investigations, or for persons that are just interested in reading about matters or topics that are currently revealed in differing forms of media, such as in the successful TV drama series "CSI." The book is formatted sequentially so that the reader can review important legal matters that are a part of most investigations and then go on to peruse the elements of basic electrical principles as they apply to certain types of fire and fault losses. These beginning chapters set a broad stage for the various areas of computing that follow. The book does not necessarily have to be read in the order that it was written. In a sense, the reader may choose to use the book as a reference book. The chapters were written, for the most part, to be able to stand alone, as monographs. There are many chapters that review a broad range of more common topics and there are chapters concerned with more esoteric areas of computing and electronics. Some of these chapters discuss the high-tech methods that are sometimes deployed by thieves, terrorists, pedophiles, stalkers, etc. All of the co-authors reflect their experience as individuals that work closely with the criminal justice and civil institutions.
Author: Alexander Lubotzky
Publisher: Birkhäuser
ISBN: 3034889658
Category : Mathematics
Languages : en
Pages : 463
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Book Description
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.
Author: Gerd Fischer
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 904
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Book Description
Author: Lizhen Ji
Publisher: American Mathematical Soc.
ISBN: 0821848666
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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.
Author: Andrew J. Duncan
Publisher: Cambridge University Press
ISBN: 9780521465953
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Authoritative collection of surveys and papers that will be indispensable to all research workers in the area.
