Office hours with a geometric group theorist
- New Jersey: Princeton University Press, [c2007]
- 441 p.
Part 1. Groups and spaces
Part 2. Free groups
Part 3. Large scale geometry
Part 4. Examples
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. This text brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. 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.
9780691158662
Mathematics
Geomatric group theory
QA183. O44
Part 1. Groups and spaces
Part 2. Free groups
Part 3. Large scale geometry
Part 4. Examples
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. This text brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. 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.
9780691158662
Mathematics
Geomatric group theory
QA183. O44