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Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Topics in geometric group theory / (Record no. 418826)

MARC details
000 -LEADER
fixed length control field 04059cam a22002414a 4500
001 - CONTROL NUMBER
control field 11880678
003 - CONTROL NUMBER IDENTIFIER
control field ISI Library, Kolkata
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20150114132730.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 000103s2000 ilua b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0226317196 (alk. paper)
040 ## - CATALOGING SOURCE
Original cataloging agency ISI Library
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.2
Edition number 23
Item number L111
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name La Harpe, Pierre de.
245 10 - TITLE STATEMENT
Title Topics in geometric group theory /
Statement of responsibility, etc Pierre de la Harpe.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Chicago :
Name of publisher, distributor, etc University of Chicago Press,
Date of publication, distribution, etc c2000.
300 ## - PHYSICAL DESCRIPTION
Extent vi, 310 p. :
Other physical details ill. ;
Dimensions 24 cm.
490 ## - SERIES STATEMENT
Series statement Chicago lectures in mathematics
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references (p. 265-294) and indexes.
505 ## - FORMATTED CONTENTS NOTE
Formatted contents note I. Gauss' circle problem and Polya's random walks on lattices --<br/>The circle problem --<br/>Polya's recurrence theorem --<br/>II. Free products and free groups --<br/>Free Products of Groups --<br/>The Table-Tennis Lemma (Klein's criterion) and examples of free products --<br/>III. Finitely-generated groups --<br/>Finitely-generated and infinitely-generated groups --<br/>Uncountably many groups with two generators (B.H. Neumann's method) --<br/>On groups with two generators --<br/>On finite quotients of the modular group --<br/>IV. Finitely-generated groups viewed as metric spaces --<br/>Word lengths and Cayley graphs --<br/> Quasi-isometries --<br/>V. Finitely-presented groups --<br/>Finitely-presented groups --<br/>The Poincare theorem on fundamental polygons --<br/>On fundamental groups and curvature in Riemannian geometry --<br/>Complement on Gromov's hyperbolic groups --<br/>VI. Growth of finitely-generated groups --<br/>Growth functions and growth series of groups --<br/>Generalities on growth types --<br/>Exponential growth rate and entropy --<br/>VII. Groups of exponential or polynomial growth --<br/>On groups of exponential growth --<br/>On uniformly exponential growth --<br/>On groups of polynomial growth --<br/>Complement on other kinds of growth --<br/>VIII. The first Grigorchuk group --<br/>Rooted d-ary trees and their automorphisms --<br/>The group [Gamma] as an answer to one of Burnside's problems --<br/>On some subgroups of [Gamma] --<br/>Congruence subgroups --<br/>Word problem and non-existence of finite presentations --<br/>Growth --<br/>Exercises and complements--<br/><br/>References--<br/>Index of research problems--<br/>Subject index.
520 ## - SUMMARY, ETC.
Summary, etc "Groups as abstract structures were first recognized by mathematicians in the nineteenth century. Groups are, of course, sets given with appropriate "multiplications," and they are often given together with actions on interesting geometric objects. But groups are also interesting geometric objects by themselves. More precisely, a finitely-generated group can be seen as a metric space, the distance between two points being defined "up to quasi-isometry" by some "word length," and this gives rise to a very fruitful approach to group theory." "In this book, Pierre de la Harpe provides a concise and engaging introduction to this approach, 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 uses a hands-on presentation style, illustrating key concepts of geometric group theory with numerous concrete examples." "The first five chapters present basic combinatorial and geometric group theory in a unique 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," an infinite finitely-generated torsion group of intermediate growth which is becoming more and more important in group theory. 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 questions in the field. An extensive list of references directs readers to more advanced results as well as connections with other subjects. Book jacket."--Jacket.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Geometric group theory.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type Books
Holdings
Lost status Not for loan Home library Current library Date acquired Cost, normal purchase price Full call number Accession Number Original Price Koha item type
    ISI Library, Kolkata ISI Library, Kolkata 04/12/2014 1451.94 512.2 L111 C26314 USD 23.46 Books
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