M. Sc. Enrico Toffoli (15.30 - 16.00)

Rho invariants for manifolds with boundary and low dimensional topology.

Abstract: In a series of two papers written between 2000 and 2002, Paul Kirk and Matthias Lesch defined an extension of the classical Atiyah-Patodi-Singer rho invariants to manifolds with boundary. Although they proved gluing formulas relating them to their classical counterparts, these invariants remain difficult to compute and have found scarce or no application so far.
In this talk, I wish to illustrate an ongoing project that aims to apply the Kirk-Lesch rho invariants to low-dimensional situations. In particular, I will use them to define a new invariant for links in the 3-sphere and present a formula comparing this invariant to the already studied multivariable signature.