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Concordances from differences of torus knots to $L$-space knots


Author: Samantha Allen
Journal: Proc. Amer. Math. Soc. 148 (2020), 1815-1827
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/proc/14833
Published electronically: December 30, 2019
MathSciNet review: 4069217
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Abstract: It is known that connected sums of positive torus knots are not concordant to $L$-space knots. Here we consider differences of torus knots. The main result states that the subgroup of the concordance group generated by two positive torus knots contains no nontrivial $L$-space knots other than the torus knots themselves. Generalizations to subgroups generated by more than two torus knots are also considered.


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Samantha Allen
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
Email: samantha.g.allen@dartmouth.edu

Received by editor(s): March 18, 2019
Received by editor(s) in revised form: August 1, 2019, and August 20, 2019
Published electronically: December 30, 2019
Communicated by: David Futer
Article copyright: © Copyright 2019 American Mathematical Society