2022/08/24 by Allison N. Miller, Mark Powell, Miller, Allison N. +1
Mathematics · #57K10 #57N35 #57N70 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2208.11571
openalex publication_date 2022/08/24 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let K be a genus one strongly invertible slice knot with nontrivial Alexander polynomial. We show that the equivariant slice genus of an equivariant connected sum #n K is at least n/4. We also formulate an equivariant algebraic concordance group, and show that the kernel of the forgetful map to the classical algebraic concordance group is infinite rank.