Khovanov homotopy type and periodic links

Maciej Borodzik, Wojciech Politarczyk, Marithania Silvero

Published 2018-07-23Version 1

Given an $m$-periodic link $L\subset S^3$, we show that the Khovanov spectrum $\X_L$ constructed by Lipshitz and Sarkar admits a group action. We relate the Borel cohomology of $\X_L$ to the equivariant Khovanov homology of $L$ constructed by the second author. The action of Steenrod algebra on the cohomology of $\X_L$ gives an extra structure of the periodic link.