Bonn Topology Group - Abstracts

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Talk

May 13, 2025
Fabian Hebestreit (Universität Bielefeld): Circle assembly in hermitian K-theory
jt with B. Calmès, E. Dotto, Y. Harpaz, M. Land, K. Moi, D. Nardin, T. Nikolaus and W. Steimle

Abstract

Hermitian K-theory is a cousin of algebraic K-theory that replaces projective modules with unimodular forms. As such one expects many of its fundamental properties to mirror those of algebraic K-theory. In the present talk (which corresponds to the forthcoming fourth part of our paper series) I will take up the Bass-Heller-Swan decomposition, which in particular provides a calculation of the algebraic K-groups of Laurent polynomial rings. I will explain the hermitian version of it and simultaneously unify it with the Ranicki-Shaneson splitting describing the L-groups of such polynomial rings. I will also give an account of the Rothenberg sequences and combining the two one obtains an identification of the difference between non-connective algebraic K-theory and its hermitian analogue with the variant of L-theory that occurs in the Farrell-Jones conjecture.

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