Given a knot in , let be the double branched cover of over . We show there is a spectral sequence whose page is , for a –vector space of dimension two, and whose page is isomorphic to , as –modules. As a consequence, we deduce a rank inequality between the knot Floer homologies and .
"A rank inequality for the knot Floer homology of double branched covers." Algebr. Geom. Topol. 12 (4) 2127 - 2178, 2012. https://doi.org/10.2140/agt.2012.12.2127