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Article overview
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Null surgery on knots in L-spaces | | Yi Ni
; Faramarz Vafaee
; | | Date: |
25 Aug 2016 | | 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
$Ksubset Y$ has a Dehn surgery to $S^1 imes S^2$, then $K$ is rationally
fibered. In the case that $K$ admits some $S^1 imes S^2$ surgery, $K$ is
Floer simple, that is, the rank of $hat{HFK}(Y,K)$ 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 $b_1>0$). | | Source: | arXiv, 1608.7050 | | Services: | Forum | Review | PDF | Favorites | |
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