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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.)