English

Counterexamples to Allen's conjectures

Geometric Topology 2024-07-18 v1

Abstract

We show that the torus knots T(2,5)T(2,5) and T(2,9)T(2,9) bound smooth M\"{o}bius bands in the 4-ball whose double branched covers are negative definite, giving counterexamples to Conjectures 1.6 and 1.8 of Allen in [New York J. Math. 29 (2023) 1038-1059].

Cite

@article{arxiv.2407.12049,
  title  = {Counterexamples to Allen's conjectures},
  author = {Kouki Sato},
  journal= {arXiv preprint arXiv:2407.12049},
  year   = {2024}
}

Comments

4 pages, 3 figures

R2 v1 2026-06-28T17:43:35.481Z