Knots with many minimal genus Seifert surfaces

Abstract

Roberts proved that a family of alternating, arborescent, prime knots each have at least $2^{2n-1}$ distinct minimal genus Seifert surfaces, where $n$ is the genus of the knot in question. We give a subfamily of these knots that have exactly this many minimal genus Seifert surfaces.

3 pages, 2 figures. Version 2: corrections arising from a difference in definitions, reference added

References in corpus (1)

• Minimal genus Seifert surfaces for alternating links