The Equivariant Genera of Marked Strongly Invertible Knots Associated with 2-Bridge Knots
Abstract
A marked strongly invertible knot is a triple (K,h,δ) of a knot K in S3, a strong inversion h of K, and a subarc δ⊂Fix(h)≅S1 bounded by Fix(h)∩K≅S0. An invariant Seifert surface for (K,h,δ) is an h-invariant Seifert surface for K that intersects Fix(h) in the arc δ. In this paper, we completely determine the equivariant genus (the minimum of the genera of invariant Seifert surfaces for (K,h,δ)) of every marked strongly invertible knot (K,h,δ) with K a 2-bridge knot.
Fields of Study & Subjects
Geometric and Algebraic Topology
Analytic and geometric function theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- The Michigan Mathematical Journal
- Volume
- -1
- Issue
- -1
- Publication date
- 1 January 2026