Efficient calculations of S-invariants for links

2025/08/15 by Schuetz, Dirk
#57K18 (Primary) 57K10 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2508.11373

Abstract

We describe an algorithm that can effectively calculate the s-invariant of a link as defined by Beliakova and Wehrli. Our computations show that this cannot be done by merely calculating the E_∞-page of the Bar-Natan--Lee--Turner spectral sequence. Our methods also work for s-invariants coming from sl(3)-link homology.

Citations

• On Variations of s-invariants from sl(3)-link homology
• A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms
• On an integral version of the Rasmussen invariant
• A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds
• A fast algorithm for calculating s-invariants
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Fast Khovanov Homology Computations
• Khovanov homology and the slice genus

Related

• On Variations of s-invariants from sl(3)-link homology
• A family of link concordance invariants from perturbed sl(n) homology
• A Casson-Lin type invariant for links
• On invariants of link maps in dimension four
• Gauss-type formulas for link map invariants