Khovanov homology and strongly invertible knots
Strong inversions are a class of order-2 symmetries of knots in S^3. Building on work of Lidman-Manolescu, Stoffregen-Zhang, and others, we will describe a relationship between the Khovanov homology of a knot with a strong inversion and its quotients by the inversion. We will also give a modest application to surfaces in 4-space. This is joint work with Sucharit Sarkar. While there is no symplectic geometry in the talk, many of the ideas come from or may be useful in Floer-theoretic settings.