An Additivity Theorem for cobordism categories, with applications to Hermitian K-theory

The goal of this talk is to explain that Genauer's computation of the cobordism category with boundaries is a precise analogue of Waldhausen's additivity theorem in algebraic K-theory, and to give a new, parallel proof of both results. The same proof technique also applies to cobordism categories of Poincaré chain complexes in the sense of Ranicki. Here we obtain that its classifying space is the infinite loop space of a non-connective spectrum which has similar properties as Schlichting's Grothendieck-Witt spectrum when 2 is invertible; but it turns out that these properties still hold even if 2 is not invertible. This talk is partially based on joint work with B. Calmès, E. Dotto, Y. Harpaz, F. Hebestreit, M. Land, K. Moi, D. Nardin and Th. Nikolaus.