Finiteness of Compact Maximal Flats of Bounded Volume

Periodic Maximal Flats Are Not Peripheral

We prove that every non-positively curved locally symmetric manifold M of finite volume contains a compact set K such that no periodic maximal flat in M can be homotoped out of K. Este art́ıculo está dedicado a Cloe y a la madre que la parió.

Aspherical Manifolds with Relatively Hyperbolic Fundamental Groups

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, acylindricity, a...

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

HECKE ORBITS OF COMPACT MAXIMAL FLATS IN ZGLn(Z)nGLn(R)=On

Homotopy Type and Volume of Locally Symmetric Manifolds

We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M . When M is non-compact, R is homotopically equivalent to M , while when M is compact, R is homotopically equivalent to M \ N , where N is a finite union of submanifolds of fairly smaller dimensions. This expresses h...