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What is the geometric interpretation of the first Hochschild homology group of path algebra constructed from a directed graph?

Let $\mathcal{G} = (V, E, s, t)$ is a directed graph, where $V$ - the set of its vertices, $E$ - the set of its edges, $s: E \rightarrow V, s((v_1, v_2)) = v_1$ and $t: E \rightarrow V, s((v_1, v_2)) =...
Alexander's user avatar
4 votes
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158 views

Describing the THH of function spectra?

Are there any results describing the $THH$ of spectra of the form $F(X, E)$ where $X$ is a space (say, finite CW) and $E$ is a (nice enough) ring spectrum? I'm happy to put various (further, or ...
John Greenwood's user avatar
3 votes
0 answers
300 views

Hochschild homology of a tensor algebra modulo a two-sided ideal

Let $V$ is a module over a field $k$, and $A=T(V)$ the tensor algebra generated by $V$. The Hochschild homology $HH_*(A)$ has been determined by Loday and Quillen in their paper "Cyclic homology and ...
anonymous's user avatar