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

Samantha Allen

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

Geometric Topology 2019-09-16 v2

Authors: Samantha Allen

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.

Keywords

concordance group torus knots L-space knots positive torus knots concordance

Cite

@article{arxiv.1710.10664,
  title  = {Concordances from differences of torus knots to $L$-space knots},
  author = {Samantha Allen},
  journal= {arXiv preprint arXiv:1710.10664},
  year   = {2019}
}

Comments

12 pages, 2 figures, v2. corrections and improved exposition following referee's comments. To appear in Proc. Amer. Math. Soc

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

Abstract

Keywords

Cite

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