Office hours with a geometric group theorist

Machine generated contents note: pt. 1 GROUPS AND SPACES
1.Groups /​ Dan Margalit
1.1.Groups
1.2.Infinite groups
1.3.Homomorphisms and normal subgroups
1.4.Group presentations
2.... and Spaces /​ Dan Margalit
2.1.Graphs
2.2.Metric spaces
2.3.Geometric group theory: groups and their spaces
pt. 2 FREE GROUPS
3.Groups Acting on Trees /​ Dan Margalit
3.1.The Farey tree
3.2.Free actions on trees
3.3.Non-free actions on trees
4.Free Groups and Folding /​ Matt Clay
4.1.Topological model for the free group
4.2.Subgroups via graphs
4.3.Applications of folding
5.The Ping-Pong Lemma /​ Johanna Mangahas
5.1.Statement, proof, and first examples using ping-pong
5.2.Ping-pong with Mobius transformations
5.3.Hyperbolic geometry
5.4.Final remarks
6.Automorphisms of Free Groups /​ Matt Clay
6.1.Automorphisms of groups: first examples
6.2.Automorphisms of free groups: a first look
6.3.Train tracks
Contents note continued: pt. 3 LARGE SCALE GEOMETRY
7.Quasi-isometries /​ Anne Thomas
7.1.Example: the integers
7.2.Bi-Lipschitz equivalence of word metrics
7.3.Quasi-isometric equivalence of Cayley graphs
7.4.Quasi-isometries between groups and spaces
7.5.Quasi-isometric rigidity
8.Dehn Functions /​ Timothy Riley
8.1.Jigsaw puzzles reimagined
8.2.A complexity measure for the word problem
8.3.Isoperimetry
8.4.A large-scale geometric invariant
8.5.The Dehn function landscape
9.Hyperbolic Groups /​ Moon Duchin
9.1.Definition of hyperbolicity
9.2.Examples and nonexamples
9.3.Surface groups
9.4.Geometric properties
9.5.Hyperbolic groups have solvable word problem
10.Ends of Groups /​ John Meier
10.1.An example
10.2.The number of ends of a group
10.3.Semidirect products
10.4.Calculating the number of ends of the braid groups
10.5.Moving beyond counting
11.Asymptotic Dimension /​ Greg Bell
11.1.Dimension
Contents note continued: 11.2.Motivating examples
11.3.Large-scale geometry
11.4.Topology and dimension
11.5.Large-scale dimension
11.6.Motivating examples revisited
11.7.Three questions
11.8.Other examples
12.Growth of Groups /​ Eric Freden
12.1.Growth series
12.2.Cone types
12.3.Formal languages and context-free grammars
12.4.The DSV method
pt. 4 EXAMPLES
13.Coxeter Groups /​ Adam Piggott
13.1.Groups generated by reflections
13.2.Discrete groups generated by reflections
13.3.Relations in finite groups generated by reflections
13.4.Coxeter groups
14.Right-Angled Artin Groups /​ Matt Clay
14.1.Right-angled Artin groups as subgroups
14.2.Connections with other classes of groups
14.3.Subgroups of right-angled Artin groups
14.4.The word problem for right-angled Artin groups
15.Lamplighter Groups /​ Jennifer Taback
15.1.Generators and relators
15.2.Computing word length
15.3.Dead end elements
Contents note continued: 15.4.Geometry of the Cayley graph
15.5.Generalizations
16.Thompson's Group /​ Sean Cleary
16.1.Analytic definition and basic properties
16.2.Combinatorial definition
16.3.Presentations
16.4.Algebraic structure
16.5.Geometric properties
17.Mapping Class Groups /​ Dan Margalit
17.1.A brief user's guide to surfaces
17.2.Homeomorphisms of surfaces
17.3.Mapping class groups
17.4.Dehn twists in the mapping class group
17.5.Generating the mapping class group by Dehn twists
18.Braids /​ Aaron Abrams
18.1.Getting started
18.2.Some group theory
18.3.Some topology: configuration spaces
18.4.More topology: punctured disks
18.5.Connection: knot theory
18.6.Connection: robotics
18.7.Connection: hyperplane arrangements
18.8.A stylish and practical finale.

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.

https://press.princeton.edu/books/paperback/9780691158662/office-hours-with-a-geometric-group-theorist