Office Hours with a Geometric Group Theorist / / ed. by Dan Margalit, Matt Clay.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017
• MitwirkendeR: Abrams, Aaron,; Bell, Greg,; Bell, Robert W.,; Brendle, Tara,; Childers, Leah,; Clay, Matt,; Cleary, Sean,; Duchin, Moon,; Freden, Eric,; Koban, Nic,; Mangahas, Johanna,; Margalit, Dan,; Meier, John,; Piggott, Adam,; Riley, Timothy,; Taback, Jennifer,; Thomas, Anne,
• HerausgeberIn: Clay, Matt,; Margalit, Dan,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2017]; ©2017
• Year of Publication: 2017
• Edition: Pilot project,eBook available to selected US libraries only
• Language: English
• Physical Description: 1 online resource (456 p.) :; 136 color illus. 2 halftones. 86 line illus. 2 tables.

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.

Table of Contents

Frontmatter -- Contents -- Preface -- Acknowledgments -- Part 1. Groups and Spaces -- 1. Groups -- 2. ... and Spaces -- Part 2. Free Groups -- 3. Groups Acting on Trees -- 4. Free Groups and Folding -- 5. The Ping-Pong Lemma -- 6. Automorphisms of Free Groups -- Part 3. Large Scale Geometry -- 7. Quasi-isometries -- 8. Dehn Functions -- 9. Hyperbolic Groups -- 10. Ends of Groups -- 11. Asymptotic Dimension -- 12. Growth of Groups -- Part 4. Examples -- 13. Coxeter Groups -- 14. Right-Angled Artin Groups -- 15. Lamplighter Groups -- 16. Thompson's Group -- 17. Mapping Class Groups -- 18. Braids -- Bibliography -- Index