Tootfinder

This https://arxiv.org/abs/2210.08055 has been replaced.
link: https://scholar.google.com/scholar?q=a

Concordances of sums of alternating torus knots and their mirrors to $L$-space knots
Continuing the work of Zemke, Livingston and Allen, we consider when linear combinations of torus knots are concordant to $L$-space knots. We begin by proving Allen's conjecture for alternating torus knots. That is, we prove that a linear combination of alternating torus knots is concordant to an $L$-space knot if and only if the connected sum is a single torus knot. Then we establish a necessary condition for when a linear combination of torus knots is concordant to an $L$-space knot.

This https://arxiv.org/abs/2210.08055 has been replaced.
link: https://scholar.google.com/scholar?q=a

Concordances of sums of alternating torus knots and their mirrors to $L$-space knots
Continuing the work of Zemke, Livingston and Allen, we consider when linear combinations of torus knots are concordant to $L$-space knots. We begin by proving Allen's conjecture for alternating torus knots. That is, we prove that a linear combination of alternating torus knots is concordant to an $L$-space knot if and only if the connected sum is a single torus knot. Then we establish a necessary condition for when a linear combination of torus knots is concordant to an $L$-space knot.

This https://arxiv.org/abs/2310.19648 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Special Alternating Knots are Band Prime
We prove that a special alternating knot does not decompose as a non-trivial band sum. This restricts concordances from special alternating knots, and we conjecture that special alternating knots are ribbon concordance minimal. We verify our conjecture in many cases. This work is motivated by another conjecture of Owens and the second author, which posits that the set of alternating knots is downward closed under ribbon concordance.