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

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.

arXiv comment12 pages, 2 figures, v2. corrections and improved exposition following referee's comments. To appear in Proc. Amer. Math. Soc