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A note on the concordance invariants epsilon and upsilon


Author: Jennifer Hom
Journal: Proc. Amer. Math. Soc. 144 (2016), 897-902
MSC (2010): Primary 57M25, 57N70, 57R58
DOI: https://doi.org/10.1090/proc/12706
Published electronically: May 28, 2015
MathSciNet review: 3430863
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Abstract: Ozsváth-Stipsicz-Szabó recently defined a one-parameter family $\Upsilon _K(t)$ of concordance invariants associated to the knot Floer complex. We compare their invariant to the $\{ -1, 0, 1\}$-valued concordance invariant $\varepsilon (K)$, which is also associated to the knot Floer complex. In particular, we give an example of a knot $K$ with $\Upsilon _K(t) \equiv 0$ but $\varepsilon (K) \neq 0$.


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Additional Information

Jennifer Hom
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
MR Author ID: 923914
ORCID: 0000-0003-4839-8276
Email: hom@math.columbia.edu

Received by editor(s): September 28, 2014
Received by editor(s) in revised form: December 29, 2014
Published electronically: May 28, 2015
Additional Notes: The author was partially supported by NSF grant DMS-1307879.
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society