Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 15, 2019 | Submitted
Journal Article Open

Null surgery on knots in L-spaces


Let K be a knot in an L-space Y with a Dehn surgery to a surface bundle over S¹. We prove that K is rationally fibered, that is, the knot complement admits a fibration over S¹. As part of the proof, we show that if K C Y has a Dehn surgery to S¹ x S², then K is rationally fibered. In the case that K admits some S¹ x S² surgery, K is Floer simple, that is, the rank of HFK(Y,K) is equal to the order of H₁(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 b₁ > 0).

Additional Information

© 2019 American Mathematical Society. Received by the editors May 12, 2017, and, in revised form, January 9, 2018, and January 12, 2018. Published electronically: September 23, 2019. The first author was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship. The second author was partially supported by an NSF Simons travel grant. 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.

Attached Files

Submitted - 1608.07050.pdf


Files (954.7 kB)
Name Size Download all
954.7 kB Preview Download

Additional details

August 19, 2023
October 18, 2023