Groups, graphs and trees : an introduction to the geometry of infinite groups

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Groups, graphs and trees : an introduction to the geometry of infinite groups / John Meier

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2008
形態:: xi, 231 p. ; 24 cm
シリーズ名:: London Mathematical Society student texts ; 73 <BA00194352>
著者名:: Meier, John, 1965-
ISBN:: 9780521895453 [0521895456] (: hbk)
9780521719773 [0521719771] (: pbk)
書誌ID:: BA86480989

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注記:

Includes bibliographical references (p. 227-229) and index

主題:

Infinite groups

言語:

英語

目次情報:

Preface

Cayley's Theorems / 1：

Cayley's Basic Theorem / 1.1：

Graphs / 1.2：

Symmetry Groups of Graphs / 1.3：

Orbits and Stabilizers / 1.4：

Generating Sets and Cayley Graphs / 1.5：

More Cayley Graphs / 1.6：

Symmetries of Cayley Graphs / 1.7：

Fundamental Domains and Generating Sets / 1.8：

Words and Paths / 1.9：

Groups Generated by Reflections / 2：

Groups Acting on Trees / 3：

Free Groups / 3.1：

F3 is a Subgroup of F2 / 3.2：

Free Group Homomorphisms and Group Presentations / 3.3：

Free Groups and Actions on Trees / 3.4：

The Group Z3 * Z4 / 3.5：

Free Products of Groups / 3.6：

Free Products of Finite Groups are Virtually Free / 3.7：

A Geometric View of Theorem 3.35 / 3.8：

Finite Groups Acting on Trees / 3.9：

Serre's Property FA and Infinite Groups / 3.10：

Baumslag-Solitar Groups / 4：

Words and Dehn's Word Problem / 5：

Normal Forms / 5.1：

Dehn's Word Problem / 5.2：

The Word Problem and Cayley Graphs / 5.3：

The Cayley Graph of BS(1,2) / 5.4：

A Finitely Generated, Infinite Torsion Group / 6：

Regular Languages and Normal Forms / 7：

Regular Languages and Automata / 7.1：

Not All Languages are Regular / 7.2：

Regular Word Problem? / 7.3：

A Return to Normal Forms / 7.4：

Finitely Generated Subgroups of Free Groups / 7.5：

The Lamplighter Group / 8：

The Geometry of Infinite Groups / 9：

Gromov's Corollary, aka the Word Metric / 9.1：

The Growth of Groups, I / 9.2：

Growth and Regular Languages / 9.3：

Cannon Pairs / 9.4：

Cannon's Almost Convexity / 9.5：

Thompson's Group / 10：

The Large-Scale Geometry of Groups / 11：

Changing Generators / 11.1：

The Growth of Groups, II / 11.2：

The Growth of Thompson's Group / 11.3：

The Ends of Groups / 11.4：

The Freudenthal-Hopf Theorem / 11.5：

Two-Ended Groups / 11.6：

Commensurable Groups and Quasi-Isometry / 11.7：

Bibliography

Index

Preface

Cayley's Theorems / 1：

Cayley's Basic Theorem / 1.1：

Graphs / 1.2：

Symmetry Groups of Graphs / 1.3：

Orbits and Stabilizers / 1.4：

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