On the topological 4-genus of torus knots

Abstract

We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible linear estimate of the topological slice genus for torus knots with non-maximal signature invariant.

arXiv comment19 pages, 4 figures. Second version: minor changes, accepted for publication by Transactions of the AMS

References in corpus (3)

• The degree of the Alexander polynomial is an upper bound for the topological slice genus
• Scissor equivalence for torus links
• On 2-bridge knots with differing smooth and topological slice genera

Cited by in corpus (11)

• On calculating the slice genera of 11- and 12-crossing knots
• A note on the topological slice genus of satellite knots
• On classical upper bounds for slice genera
• A sharp signature bound for positive four-braids
• Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space
• Untwisting 3-strand torus knots
• On the genus defect of positive braid knots
• On the slice genus of quasipositive knots in indefinite 4-manifolds
• Divide knots of maximal genus defect
• On the Thom conjecture in $C{P}^3$
• Positive Knots and Ribbon Concordance