Amphichiral knots with large 4-genus

2020/11/18 by Miller, Allison N. · 2 citations
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2011.09346

Abstract

For each g>0 we give infinitely many knots that are strongly negative amphichiral, hence rationally slice and representing 2-torsion in the smooth concordance group, yet which do not bound any locally flatly embedded surface in the 4-ball with genus less than or equal to g. Our examples also allow us to answer a question about the 4-dimensional clasp number of knots.

Cited by

• Constructing knots with low rational genera
• Every negative amphichiral knot is rationally slice

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