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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 $K_0(X)$ …
Vivek Shende's user avatar
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5 votes
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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 …