In a previous paper, V\'ertesi and the first author used grid-like Heegaard diagrams to define tangle Floer homology, which associates to a tangle $T$ a differential graded bimodule $\widetilde{ \mathrm{ CT}} (T)$. If $L$ is obtained by gluing together $T_1, \dotsc, T_m$, then the knot Floer homology $\hat{ \mathrm{ HFK}}(L)$ of $L$ can be recovered from $\widetilde{ \mathrm{ CT}} (T_1), \dotsc, \widetilde{ \mathrm{ CT}} (T_m)$. In the present paper, we prove combinatorially that tangle Floer homology satisfies unoriented and oriented skein relations, generalizing the skein exact triangles for knot Floer homology.
Categories: math.GT