Teoria Geométrica dos Grupos

Pré-requisitos: Basic group theory and Riemannian geometry

Topics: Groups and presentations: abelian groups, solvable groups, nilpotent groups, Jordan’s theorem, free groups and group presentations. Cayley graphs, coarse geometry, quasi-isometries, Gromov-hyperbolic spaces, hyperbolic groups, ideal boundaries and some further properties of hyperbolic groups. Coarse topology: metric cell complexes, the ends of a space, Rips complexes. Tits alternative. Growth of groups and Gromov’s theorem. Other proofs of Gromov’s theorem.


Further topics include: Quasi-isometries of nonuniform lattices in hyperbolic spaces, Schwartz Rigidity Theorem, Mostow Rigidity Theorem.


GHYS, E., DE LA HARPE, P. – Sur les groupes hyperboliques d’apres Mikhael Gromov. Progress in Maths. No. 83, Birkhauser, 1990.
BRIDSON, M., HAEFLIGER A. – Metric spaces of non-positive curvature, Springer-Verlag, Berlin, 1999.
DRUTU, C., KAPOVICH, M. – Lectures on Geometric Group Theory, preliminary version of the book at www.math.ucdavis.edu/~kapovich/EPR/ggt.pdf.