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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
5
votes
What is Known about the $K$-Theory of Fukaya Categories?
For $X$ Weinstein, it's a result of Oleg Lazarev that the map $H_n(X) \to SH(X)$ factors as
$$H_n(X) \twoheadrightarrow K_0(Fuk(X)) \to HH_\bullet(Fuk(X)) = SH_\bullet(X)$$
Here the map to $K_0(X)$ …
5
votes
0
answers
182
views
What kind of K-theory is this?
Suppose I have a triangulated category $T$, say the category of modules over a dg or $A_\infty$-algebra.
Let me write $GL(T)$ for the groupoid whose objects are all finite collections of generators …