Office hours with a geometric group theorist / edited by Matt Clay and Dan Margalit.

Format:

Book

Contributor:

Clay, Matt, editor.

Margalit, Dan, 1976- editor.

Language:

English

Subjects (All):

Geometric group theory.

Physical Description:

1 online resource (457 pages) : illustrations

Edition:

Pilot project,eBook available to selected US libraries only

Place of Publication:

Princeton, NJ : Princeton University Press, [2017]

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Acknowledgments

Part 1. Groups and Spaces

1. Groups / Clay, Matt / Margalit, Dan

2. ... and Spaces / Clay, Matt / Margalit, Dan

Part 2. Free Groups

3. Groups Acting on Trees / Margalit, Dan

4. Free Groups and Folding / Clay, Matt

5. The Ping-Pong Lemma / Mangahas, Johanna

6. Automorphisms of Free Groups / Clay, Matt

Part 3. Large Scale Geometry

7. Quasi-isometries / Margalit, Dan / Thomas, Anne

8. Dehn Functions / Riley, Timothy

9. Hyperbolic Groups / Duchin, Moon

10. Ends of Groups / Koban, Nic / Meier, John

11. Asymptotic Dimension / Bell, Greg

12. Growth of Groups / Freden, Eric

Part 4. Examples

13. Coxeter Groups / Piggott, Adam

14. Right-Angled Artin Groups / Bell, Robert W. / Clay, Matt

15. Lamplighter Groups / Taback, Jennifer

16. Thompson's Group / Cleary, Sean

17. Mapping Class Groups / Brendle, Tara / Childers, Leah / Margalit, Dan

18. Braids / Abrams, Aaron

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)

OCLC:

1029835125