3 may 2016 -- 14:30
Sala Seminari, Dipartimento di Matematica, Pisa
Abstract.
The simplicial volume is a homotopy invariant of closed manifolds - defined in terms of the singular chain complex - which measures the efficiency of representing the fundamental class by singular chains. So it gives an indication of how difficult it is to triangulate the manifold in question. It was first introduced by Gromov in the early 1980's in his proof of Mostow rigidity. Despite being a topological invariant the simplicial volume of a Riemannian manifold encodes interesting information about the Riemannian volume. Next to the geometric approach simplicial volume admits a description in terms of algebraic tools via bounded cohomology. This talk is ment to be an introduction to simplicial volume. We will give the basic definitions and derive a number of elementary properties. We will state some interesting results in this subject, trying to explain why simplicial volume is useful in the investigation of the relationship between topology and geometry of manifolds.