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Results tagged with kt.k-theory-and-homology
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user 582
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
19
votes
Book on Hochschild (co)homology
In addition to Kevin's excellent list:
Formality
The relation of Hochschild and cyclic homology with loop spaces (eg Jones' theorem)
and the circle action on Hochschild homology
operadic structure …
12
votes
What are Picard categories, where can I learn more about them, and why should I care to?
Determinants are discussed (in a language relevant to this current question) in this MO question.
One place Picard categories naturally appear is as fundamental (aka Poincare) groupoids -- specifical …
- 24.1k
43
votes
Accepted
What is the equivariant cohomology of a group acting on itself by conjugation?
I asked Dan Freed, who gave a very clean general solution to this problem (as expected).
Here it is (all mistakes in the transcription are mine of course).
The claim is that the equivariant cohomolog …
- 24.1k
7
votes
What is the equivariant cohomology of a group acting on itself by conjugation?
The cochains on G/G can be calculated as the Hochschild cochains of cochains on BG (this uses compactness of G - we'd get a kind of dual picture with Hochschild chains if we looked at free loops in a …
- 24.1k
12
votes
Accepted
Constructing Twisted K-theory
The answer is yes if you're working on the level of $\infty$-categories (and I'm pretty sure no if you're working on the level of homotopy categories). In other words, in the $\infty$-world there's no …
- 24.1k
8
votes
Accepted
References for equivariant K-theory
I like the book by Chriss and Ginzburg (Representation Theory and Complex Geometry, https://doi.org/10.1007/978-0-8176-4938-8) very much, and I think it fits many of your requirements.
- 24.1k