Office Hours with a Geometric Group Theorist

Name: Office Hours with a Geometric Group Theorist
Brand: Princeton University Press
Price: 206.95 EUR
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Matt Clay Dan Margalit(Herausgeber*in)

Princeton University Press

1. Auflage

Erschienen am 11. Juli 2017

456 Seiten

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978-1-4008-8539-8 (ISBN)

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Inhalt

Cover
Title
Copyright
Dedication
Contents
Preface
Acknowledgments
PART 1. GROUPS AND SPACES
1. Groups
1.1 Groups
1.2 Infinite groups
1.3 Homomorphisms and normal subgroups
1.4 Group presentations
2. . . . and Spaces
2.1 Graphs
2.2 Metric spaces
2.3 Geometric group theory: groups and their spaces
PART 2. FREE GROUPS
3. Groups Acting on Trees
3.1 The Farey tree
3.2 Free actions on trees
3.3 Non-free actions on trees
4. Free Groups and Folding
4.1 Topological model for the free group
4.2 Subgroups via graphs
4.3 Applications of folding
5. The Ping-Pong Lemma
5.1 Statement, proof, and first examples using ping-pong
5.2 Ping-pong with Möbius transformations
5.3 Hyperbolic geometry
5.4 Final remarks
6. Automorphisms of Free Groups
6.1 Automorphisms of groups: first examples
6.2 Automorphisms of free groups: a first look
6.3 Train tracks
PART 3. LARGE SCALE GEOMETRY
7. Quasi-isometries
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
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
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
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
11.1 Dimension
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
12.1 Growth series
12.2 Cone types
12.3 Formal languages and context-free grammars
12.4 The DSV method
PART 4. EXAMPLES
13. Coxeter Groups
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
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
15.1 Generators and relators
15.2 Computing word length
15.3 Dead end elements
15.4 Geometry of the Cayley graph
15.5 Generalizations
16. Thompson's Group
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
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
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
Bibliography
Index

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