THR of Poincaré ∞-categories

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• Julie Rasmusen (University of Warwick)
• Tuesday 18 June 2024, 16:45-17:15
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TRHW02 - International Conference

In recent years, work by Calmés–Dotto–Harpaz–Hebestreit–Land–Moi–Nardin–Nikolaus–Steimle has moved the theory of Hermitian K-theory into the framework of stable ∞-categories. I will introduce the basic ideas and notions of this new theory, but as it is often the case when working with K-theory in any form, this can be very hard to describe. I will therefore introduce a tool which might make our life a bit easier: Real Topological Hochschild Homology. I will explain the key ingredients that goes into constructing in particular the geometric fixed points of this as a functor, generalising the formula for ring spectra with anti-involution of Dotto–Moi–Patchkoria–Reeh, as well as providing a suitable version of Morita invariance in this new setting. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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