Presented by:
Wolfgang Steimle
Date:
Tuesday 21st August 2018 - 14:00 to 15:00
Venue:
INI Seminar Room 2
Abstract:
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.
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