Rank inequalities for the Heegaard Floer homology of branched covers

Abstract

Given a double cover between 3-manifolds branched along a nullhomologous link, we establish an inequality between the dimensions of their Heegaard Floer homologies. We discuss the relationship with the L-space conjecture and give some other topological applications, as well as an analogous result for sutured Floer homology.

arXiv comment25 pages. V2: minor revisions. Accepted for publication in Documenta Mathematica

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• Involutions, knots, and Floer K-theory