2022/10/14 by Dan Guyer, Guyer, Dan, Thomas Sachen +1
Computer Science · Mathematics · #57M12 Secondary: 57K10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #Primary: 57N70 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2210.08055
openalex publication_date 2022/10/14 · openalex created_date 2022/10/20 · openalex updated_date 2026/07/28
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.