Lipschitz simplicial volume of connected sums

Abstract: The simplicial voume is a homotopy invariant of manifolds, intruduced by Gromov in his proof of the Mostov rigidity theorem. However, it has applications to many other areas, such as degree theorems, knot theory and traversing vector fields. The Lipschitz simplicial volume is a metric version of this invariant, more suitable in the study of non-compact manifolds. One of the well known properties of the simplicial volume (also in the non-compact case) is its additivity with respect to connected sums in dim>2, and more generally with respect to gluings along amenable submanifolds. However, the proof does not generalise to the Lipschitz case. In this talk I will present a sketch of the proof of the additividy of the Lipschitz simplicial volume with respect to connected sums and gluings along amenable submanifolds with some additionalasphericity conditions.