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Slice knots with distinct Ozsváth-Szabó and Rasmussen invariants
Author(s):
Charles
Livingston
Journal:
Proc. Amer. Math. Soc.
136
(2008),
347-349.
MSC (2000):
Primary 57M25
Posted:
October 18, 2007
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Abstract:
As proved by Hedden and Ording, there exist knots for which the Ozsváth-Szabó and Rasmussen smooth concordance invariants, and , differ. The Hedden-Ording examples have nontrivial Alexander polynomials and are not topologically slice. It is shown in this note that a simple manipulation of the Hedden-Ording examples yields a topologically slice Alexander polynomial one knot for which and differ. Manolescu and Owens have previously found a concordance invariant that is independent of both and on knots of polynomial one, and as a consequence have shown that the smooth concordance group of topologically slice knots contains a summand isomorphic to . It thus follows quickly from the observation in this note that this concordance group contains a summand isomorphic to .
References:
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Additional Information:
Charles
Livingston
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email:
livingst@indiana.edu
DOI:
10.1090/S0002-9939-07-09276-3
PII:
S 0002-9939(07)09276-3
Keywords:
Slice knot,
Ozsv\'ath-Szab\'o invariant,
Rasmussen invariant,
polynomial one
Received by editor(s):
April 12, 2006
Posted:
October 18, 2007
Additional Notes:
The author's research was supported by the NSF
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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