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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Transverse Surgery on Knots in Contact 3-Manifolds
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by James Conway PDF
Trans. Amer. Math. Soc. 372 (2019), 1671-1707 Request permission


We study the effect of surgery on transverse knots in contact 3-manifolds. In particular, we investigate the effect of such surgery on open books, the Heegaard Floer contact invariant, and tightness. One main aim of this paper is to show that in many contexts, transverse surgery is a more natural tool than surgery on Legendrian knots.

We reinterpret contact $(\pm 1)$-surgery on Legendrian knots as transverse surgery on transverse push-offs, allowing us to give simpler proofs of known results. We give the first result on the tightness of inadmissible transverse surgery (cf. contact $(+1)$-surgery) for contact manifolds with vanishing Heegaard Floer contact invariant. In particular, inadmissible transverse $r$-surgery on the connected binding of a genus $g$ open book that supports a tight contact structure preserves tightness if $r > 2g-1$.

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Additional Information
  • James Conway
  • Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
  • MR Author ID: 1179876
  • Email:
  • Received by editor(s): March 14, 2018
  • Received by editor(s) in revised form: May 3, 2018
  • Published electronically: May 9, 2019
  • Additional Notes: The author was partially supported by NSF Grant DMS-13909073.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 1671-1707
  • MSC (2010): Primary 53D10, 57R17
  • DOI:
  • MathSciNet review: 3976573