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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance
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by Linh Truong
Proc. Amer. Math. Soc. 149 (2021), 1757-1771
DOI: https://doi.org/10.1090/proc/15212
Published electronically: February 1, 2021

Abstract:

We compute the knot Floer filtration induced by a cable of the meridian of a knot in the manifold obtained by large integer surgery along the knot. We give a formula in terms of the original knot Floer complex of the knot in the three-sphere. As an application, we show that a knot concordance invariant of Hom can equivalently be defined in terms of filtered maps on the Heegaard Floer homology groups induced by the two-handle attachment cobordism of surgery along a knot.
References
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Bibliographic Information
  • Linh Truong
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48103
  • MR Author ID: 1044085
  • Email: tlinh@umich.edu
  • Received by editor(s): July 10, 2019
  • Received by editor(s) in revised form: May 29, 2020
  • Published electronically: February 1, 2021
  • Additional Notes: The author was partially supported by NSF grant DMS-1606451.
  • Communicated by: David Futer
  • © Copyright 2021 Copyright is retained by the author, Linh Truong.
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 1757-1771
  • MSC (2020): Primary 57K18; Secondary 57N70, 57R58
  • DOI: https://doi.org/10.1090/proc/15212
  • MathSciNet review: 4242330