Obstruction to Equivariant Ribbon Concordance

A periodic link, is link in $S^3$ with action of ${\mathbb{Z}}_p$ by rotation with $2\pi \mathrm{/}p$ around a fixed unknot $U$. The equivariant Khovanov homology of periodic links has been studied in \cite{BP17}. We prove that the equivariant Khovanov homology for periodic links is functorial under equivariant cobordisms. Furthere more, we show that equivariant ribbon concordances induce a split injection on equivariant Khovanov homology.