Annular Rasmussen invariants: Properties and 3-braid classification

2019/09/19 by Martin, Gage
#20F36 #57M25 #57M27 #57Q60 #81R50 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1909.09245

Abstract

We prove that for a fixed braid index there are only finitely many possible shapes of the annular Rasmussen d_t invariant of braid closures. Applying the same perspective to the knot Floer invariant Υ_K(t), we show that for a fixed concordance genus of K there are only finitely many possibilities for Υ_K(t). Focusing on the case of 3-braids, we compute the Rasmussen s invariant and the annular Rasmussen d_t invariant of all 3-braid closures. As a corollary, we show that the vanishing/non-vanishing of the ψ invariant is entirely determined by the s invariant and the self-linking number.

Related

• Asymptotic Rasmussen Invariant
• The dealternating number and the alternation number of a closed 3-braid
• Properties of closed 3-braids
• On a Map From Pure Braids to Knots
• Annular Khovanov-Lee homology, braids, and cobordisms