Signed clasp numbers and four-genus bounds
Geometric Topology
2026-02-16 v2
Abstract
There exist knots having positive and negative four-dimensional clasp numbers zero but having four-genus, and hence clasp number, arbitrarily large. Such examples were first constructed by Allison Miller, answering a question of Juhasz-Zemke. Further examples are constructed here, complementing those of Miller in that they include examples that are of infinite order in concordance.
Keywords
Cite
@article{arxiv.2206.10432,
title = {Signed clasp numbers and four-genus bounds},
author = {Charles Livingston},
journal= {arXiv preprint arXiv:2206.10432},
year = {2026}
}
Comments
Exposition revised, figure added