2022/11/04 by Taketo Sano, Sano, Taketo, Kouki Sato +1
Mathematics · Computer Science · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2211.02494
We give a family of slice-torus invariants ssc, each defined from the c-divisibility of the reduced Lee class in a variant of reduced Khovanov homology, parameterized by prime elements c in any principal ideal domain R. For the special case (R, c) = (F[H], H) where F is any field, we prove that ssc coincides with the Rasmussen invariant sF over F. Compared with the unreduced invariants ssc defined by the first author in a previous paper, we prove that ssc = ssc for (R, c) = (F[H], H) and (ℤ, 2). However for (R, c) = (ℤ, 3), computational results show that ss3 is not slice-torus, which implies that it is linearly independent from the reduced invariants, and particularly from the Rasmussen invariants.