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A Bar-Natan homotopy type by Sano, Taketo is a scholarly article available to read on EtoBox.

What is A Bar-Natan homotopy type about?

A spatial refinement of Bar-Natan homology is given, that is, for any link diagram $D$ we construct a CW-spectrum $\mathcal{X}_{\mathit{BN}}(D)$ whose reduced cellular cochain complex gives the Bar-Natan complex of $D$. The stable homotopy type of $\mathcal{X}_{\mathit{BN}}(D)$ is a link invariant and is described as the wedge sum of the canonical cells. We conjecture that the quantum filtration of Bar-Natan homology also lifts to the spatial level, and that it leads us to a cohomotopical refinement of the $s$-invariant.

Author

Sano, Taketo

Published

2021

Language

EN