Geometric group theory / Cornelia Druţu, Michael Kapovich ; with an appendix by Bogdan Nica.

Bibliographic Details
Uniform Title:Colloquium publications (American Mathematical Society) ; v. 63.
Main Authors: Druţu, Cornelia, 1967- (Author)
Kapovich, Michael, 1963- (Author)
Other Authors: Nica, Bogdan, 1977- (writer of appendix.)
Language:English
Published: [Providence, Rhode Island] : American Mathematical Society, [2018]
Series:Colloquium publications (American Mathematical Society) ; v. 63.
Subjects:
Geometric group theory.
Group theory.
Group theory and generalizations > Special aspects of infinite or finite groups > Geometric group theory.
Group theory and generalizations > Special aspects of infinite or finite groups > Hyperbolic groups and nonpositively curved groups.
Group theory and generalizations > Special aspects of infinite or finite groups > Asymptotic properties of groups.
Group theory and generalizations > Special aspects of infinite or finite groups > Generators, relations, and presentations.
Group theory and generalizations > Special aspects of infinite or finite groups > Solvable groups, supersolvable groups.
Group theory and generalizations > Special aspects of infinite or finite groups > Nilpotent groups.
Group theory and generalizations > Special aspects of infinite or finite groups > Fundamental groups and their automorphisms.
Group theory and generalizations > Structure and classification of infinite or finite groups > Groups acting on trees.
Group theory and generalizations > Structure and classification of infinite or finite groups > Residual properties and generalizations; residually finite groups.
Manifolds and cell complexes > Low-dimensional topology > Topological methods in group theory.
Physical Description:xx, 819 pages : illustrations ; 27 cm.
Format: Book
Contents:
  • Geometry and topology
  • Metric spaces
  • Differential geometry
  • Hyperbolic space
  • Groups and their actions
  • Median spaces and spaces with measured walls
  • Finitely generated and finitely presented groups
  • Coarse geometry
  • Coarse topology
  • Ultralimits of metric spaces
  • Gromov-hyperbolic spaces and groups
  • Lattices in Lie groups
  • Solvable groups
  • Geometric aspects of solvable groups
  • The Tits Alternative
  • Gromov's Theorem
  • The Banach-Tarski Paradox
  • Amenability and paradoxical decomposition
  • Ultralimits, fixed-point properties, proper actions
  • The Stallings Theorem and accessibility
  • Proof of Stallings' Theorem using harmonic functions
  • Quasiconformal mappings
  • Groups quasiisometric to H⁷²
  • Quasiisometries of non-uniform lattices in H⁷²
  • A survey of quasiisometric rigidity
  • Appendix : three theorems on linear groups / by Bogdan Nica.