Stable homotopy refinement of quantum annular homology

Rostislav Akhmechet; Vyacheslav Krushkal; Michael Willis

doi:10.1112/s0010437x20007721

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arXiv · 2001.00077

Stable homotopy refinement of quantum annular homology

Rostislav Akhmechet·Vyacheslav Krushkal·Michael Willis

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Abstract

We construct a stable homotopy refinement of quantum annular homology, a link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq 2$ we associate to an annular link $L$ a naive $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum whose cohomology is isomorphic to the quantum annular homology of $L$ as modules over $\mathbb{Z}[\mathbb{Z}/r\mathbb{Z}]$. The construction relies on an equivariant version of the Burnside category approach of Lawson, Lipshitz and Sarkar. The quotient under the cyclic group action is shown to recover the stable homotopy refinement of annular Khovanov homology. We study spectrum level lifts of structural properties of quantum annular homology.

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BibTeX RIS

Rostislav Akhmechet, Vyacheslav Krushkal, Michael Willis. 2019-12-31. Stable homotopy refinement of quantum annular homology. https://doi.org/10.1112/s0010437x20007721

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