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For questions about cyclic homology of associative algebras and related concepts.
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Failure of periodic cyclic homology to be a localizing invariant
A localizing invariant $E: dgcat_{sm} \rightarrow Ch_k$ from small dg categories to chain complexes over a field $k$ (say $k = \mathbb{C}$) is a dg functor which sends localization sequences to exact …
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Topological invariance of periodic cyclic homology of stacks
Goodwillie proved (in Cyclic homology, derivations, and the free loopspace) that the periodic cyclic homology of a connective dg algebra is that of its reduced classical ring. Preygel proved (in Ind- …