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Computing topological Hochschild homology using twisted theories. (English) Zbl 07272547
Srinivas, V. (ed.) et al., \(K\)-theory. Proceedings of the international colloquium, Mumbai, 2016. New Delhi: Hindustan Book Agency; Mumbai: Tata Institute of Fundamental Research (ISBN 978-93-86279-74-3/hbk). Studies in Mathematics. Tata Institute of Fundamental Research 23, 367-393 (2019).
Summary: The study of twisted theories generalizes earlier definitions of twisted \(K\) theory and cohomology with local coefficients on one hand and the Thom spectra associated to spherical fibrations on the other hand. We briefly recall this formulation for arbitrary \(E_\infty\)-ring spectra. Apart from geometric considerations, the theory is amenable to detection of ring structures in module spectra and computation of invariants like topological Hochschild homology. We describe a computation using the 3-sphere.
For the entire collection see [Zbl 1435.19001].
MSC:
19L50 Twisted \(K\)-theory; differential \(K\)-theory
19L64 Geometric applications of topological \(K\)-theory
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
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