Bonn Topology Group - Abstracts

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May 14th 2019
Markus Land (Universität Regensburg): On the K-theory of pullbacks


I will report on joint work with Georg Tamme. We investigate the question when a localizing invariant E, such as K-theory or (variants of) topological Hochschild homology, applied to a pullback diagram of ring spectra is again a pullback diagram. I will first explain our main theorem, which associates to a pullback diagram of ring spectra a refined diagram in which a new ring spectrum appears. This new ring measures effectively whether E applied to the original diagram is a pullback. I will then derive immediate consequences for invariants which we call truncating, and to excision in K-theory. I will finish the talk with some examples where the new ring can be described explicitly and indicate its use for explicit computations.

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