Determining the doubly slice genera of prime knots with up to 12 crossings

2021/04/21 by Karageorghis, Lucia P., Swenton, Frank
#57K10 #57K45 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2104.10756

Abstract

For a knot K, the doubly slice genus g_ds(K) is the minimal g such that K divides a closed, orientable, and unknotted surface of genus g embedded in S⁴. In this paper, we identify the doubly slice genera of 2909 of the 2977 prime knots which have a crossing number of 12 or fewer.

Related

• A lower bound for the doubly slice genus from signatures
• The smooth 4-genus of (the rest of) the prime knots through 12 crossings
• Knots with many minimal genus Seifert surfaces
• Genera of knots in the complex projective plane
• On knots that divide ribbon knotted surfaces