TL;DR
This paper shows that quantum Hochschild homology, related to annular Khovanov homology, can be understood as a composition of familiar operations, providing a simple proof of its invariance for annular links.
Contribution
It clarifies the structure of quantum Hochschild homology as a composition of known operations and offers a concise proof of its invariance for annular links.
Findings
Quantum Hochschild homology is a composition of two familiar operations.
Provides a short proof that it is an invariant of annular links.
Connects to previous work on deformations of annular Khovanov homology.
Abstract
Beliakova-Putyra-Wehrli studied various kinds of traces, in relation to annular Khovanov homology. In particular, to a graded algebra and a graded bimodule over it, they associate a quantum Hochschild homology of the algebra with coefficients in the bimodule, and use this to obtain a deformation of the annular Khovanov homology of a link. A spectral refinement of the resulting invariant was recently given by Akhmechet-Krushkal-Willis. In this short note we observe that quantum Hochschild homology is a composition of two familiar operations, and give a short proof that it gives an invariant of annular links, in some generality. Much of this is implicit in Beliakova-Putyra-Wehrli's work.
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