Simplicial volume is a homotopy invariant of oriented closed connected manifolds introduced by Gromov in his proof of Mostow rigidity. On the one hand, the simplicial volume of a Riemannian manifold encodes non-trivial information about the Riemannian volume; on the other hand, simplicial volume can be described in terms of a certain functional analytic version of homological algebra (bounded cohomology). In this article we survey important properties and applications of simplicial volume as well as useful techniques for working with simplicial volume.
simplicial volume, minimal volume, bounded cohomology
Primary: 53C23, 57R99
|9th September 2010
|17th December 2010
|1st May 2011