Homological actions on sutured Floer homology

Abstract

We define the action of the homology group $H_1(M,\partial M)$ on the sutured Floer homology $SFH(M,\gamma )$. It turns out that the contact invariant $EH(M,\gamma ,\xi )$ is usually sent to zero by this action. This fact allows us to refine an earlier result proved by Ghiggini and the author. As a corollary, we classify knots in $#^n(S^1\times S^2)$ which have simple knot Floer homology groups: They are essentially the Borromean knots.

17 pages, 2 figures

References in corpus (2)

• Floer homology and knot complements
• Lens space surgeries and L-space homology spheres

Cited by in corpus (1)

• Combinatorial Sutured TQFT as Exterior Algebra