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Null surgery on knots in L-spaces

Ni, Yi and Vafaee, Faramarz (2018) Null surgery on knots in L-spaces. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20180308-071823523

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Abstract

Let K be a knot in an L-space Y with a Dehn surgery to a surface bundle over S^1. We prove that K is rationally fibered, that is, the knot complement admits a fibration over S^1. As part of the proof, we show that if K C Y has a Dehn surgery to S^1 x S^2, then K is rationally fibered. In the case that K admits some S^1 x S^2 surgery, K is Floer simple, that is, the rank of HFK(Y,K) is equal to the order of H_1(Y). By combining the latter two facts, we deduce that the induced contact structure on the ambient manifold Y is tight. In a different direction, we show that if K is a knot in an L-space Y, then any Thurston norm minimizing rational Seifert surface for K extends to a Thurston norm minimizing surface in the manifold obtained by the null surgery on K (i.e., the unique surgery on K with b_1 > 0).


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1608.07050arXivDiscussion paper
Additional Information:Submitted on 25 Aug 2016 (v1), last revised 14 Jan 2018 (this version, v2). We are grateful to Kenneth Baker for pointing out Remark 3.2 to us, to Matthew Hedden for his input to Proposition 1.7, to Tye Lidman for helpful conversations, and to Jacob Rasmussen for pointing out a mistake in an earlier draft. We thank the referee for valuable remarks and a thoughtful review. Y. N. was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship; F. V. was partially supported by an NSF Simons travel grant.
Funders:
Funding AgencyGrant Number
NSFDMS-1103976
NSFDMS-1252992
Alfred P. Sloan FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20180308-071823523
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180308-071823523
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85190
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:08 Mar 2018 15:59
Last Modified:08 Mar 2018 15:59

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