Semigroups of L-space knots and nonalgebraic iterated torus knots

2016/03/29 by Wang, Shida · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1603.08877

Abstract

Algebraic knots are known to be iterated torus knots and to admit L-space surgeries. However, Hedden proved that there are iterated torus knots that admit L-space surgeries but are not algebraic. We present an infinite family of such examples, with the additional property that no nontrivial linear combination of knots in this family is concordant to a linear combination of algebraic knots. The proof uses the Ozsvath-Stipsicz-Szabo Upsilon function, and also introduces a new invariant of L-space knots, the formal semigroup.

Cited by

• An infinite family of strongly invertible L-space knots without Khovanov thin surgery

Related

• Hyperbolic L-space knots and their formal semigroups
• Topological Representations of Free Numerical Semigroups via Iterated Torus Knots
• Two curious strongly invertible L-space knots
• Concordances of sums of alternating torus knots and their mirrors to L-space knots
• Knots not concordant to L-space knots