Giuseppe Bargagnati (Università di Bologna)

Abstract: The simplicial volume is a homotopy invariant of manifolds introduced by Gromov in 1982. Despite being purely homotopic in nature, the simplicial volume is deeply sensitive to the geometric structures that a manifold can carry: for example, it is positive for compact manifolds which carry a hyperbolic metric, and it furnishes estimates and bounds for many other significant invariants which come from Riemannian geometry (for instance, the minimal volume). In the first part of this talk, I will define the simplicial volume for compact and non compact manifolds, state some of its properties and focus on the values that this invariant can assume in every dimension (i.e., on its spectrum). In the second part of the talk, I will focus on the spectrum of simplicial volume of open 3-manifolds, which remains mysterious to these days.