Homological actions on sutured Floer homology

Yi Ni

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arXiv · 1010.2808

Homological actions on sutured Floer homology

Yi Ni

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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.

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Yi Ni. 2010-10-14. Homological actions on sutured Floer homology. https://arxiv.org/abs/1010.2808

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