Certain connect sums of torus knots with infinitely many non-characterizing slopes

Abstract

For a knot $K,$ a slope $r$ is said to be characterizing if for no other knot $J$ does $r$-framed surgery along $J$ yield the same manifold as $r$-framed surgery on $K.$ Applying a condition of Baker and Motegi, we show that the knots $T_{2,2n+3}\#T_{-2,2n+1}$ have infinitely many non-characterizing slopes.

arXiv comment28 pages, 24 figures; revised to clarify the orientability of the banded annulus