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Proceedings of the American Mathematical Society

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A refinement of the Ozsváth-Szabó large integer surgery formula and knot concordance


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
Published electronically: February 1, 2021
MathSciNet review: 4242330
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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.


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Additional 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
Article copyright: © Copyright 2021 Copyright is retained by the author, Linh Truong.