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Homological actions on sutured Floer homology

Ni, Yi (2014) Homological actions on sutured Floer homology. Mathematical Research Letters, 21 (5). pp. 1177-1197. ISSN 1073-2780. doi:10.4310/MRL.2014.v21.n5.a12.

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We define the action of the homology group H_1(M,∂M) on the sutured Floer homology SFH(M,γ). It turns out that the contact invariant EH(M,γ,ξ) 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×S^2) which have simple knot Floer homology groups: They are essentially the Borromean knots. This answers a question of Ozsváth. In a different direction, we show that the only links in S^3 with simple knot Floer homology groups are the unlinks.

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Additional Information:© 2014 International Press of Boston, Inc. Received May 4, 2013. This work was carried out when the author participated the “Homology Theories of Knots and Links” program at MSRI and when the author visited Princeton University. The author wishes to thank MSRI and David Gabai for their hospitality. The author was partially supported by an AIM Five-Year Fellowship and NSF grant number DMS-1021956.
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AIM Five-Year FellowshipUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20150220-113128978
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55051
Deposited By: Ruth Sustaita
Deposited On:20 Feb 2015 20:52
Last Modified:10 Nov 2021 20:41

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