English

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

R2 v1 2026-06-24T11:58:37.650Z