Null surgery on knots in L-spaces

Author:

Ni Yi,Vafaee Faramarz

Abstract

Let K K be a knot in an L-space Y Y with a Dehn surgery to a surface bundle over S 1 S^1 . We prove that K K is rationally fibered, that is, the knot complement admits a fibration over S 1 S^1 . As part of the proof, we show that if K Y K\subset Y has a Dehn surgery to S 1 × S 2 S^1 \times S^2 , then K K is rationally fibered. In the case that K K admits some S 1 × S 2 S^1 \times S^2 surgery, K K is Floer simple, that is, the rank of H F K ^ ( Y , K ) \widehat {HFK}(Y,K) is equal to the order of H 1 ( Y ) H_1(Y) . By combining the latter two facts, we deduce that the induced contact structure on the ambient manifold Y Y is tight.

In a different direction, we show that if K K is a knot in an L-space Y Y , then any Thurston norm minimizing rational Seifert surface for K K extends to a Thurston norm minimizing surface in the manifold obtained by the null surgery on K K (i.e., the unique surgery on K K with b 1 > 0 b_1>0 ).

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference49 articles.

1. Two applications of twisted Floer homology;Ai, Yinghua;Int. Math. Res. Not. IMRN,2009

2. An unexpected surgery construction of a lens space;Bailey, James;Pacific J. Math.,1977

3. Some knots in 𝑆¹×𝑆² with lens space surgeries;Baker, Kenneth L.;Comm. Anal. Geom.,2016

4. Cabling, contact structures and mapping class monoids;Baker, Kenneth L.;J. Differential Geom.,2012

5. [Ber] John Berge, Some knots with surgeries yielding lens spaces, Unpublished manuscript.

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