English

On the secondary Upsilon invariant

Geometric Topology 2021-08-25 v1

Abstract

In this paper we construct an infinite family of knots with vanishing Upsilon invariant Υ\Upsilon, although their secondary Upsilon invariants Υ2\Upsilon^2 show that they are linearly independent in the smooth knot concordance group. We also prove a conjecture in a paper by Allen.

Keywords

Cite

@article{arxiv.1805.09376,
  title  = {On the secondary Upsilon invariant},
  author = {Xiaoyu Xu},
  journal= {arXiv preprint arXiv:1805.09376},
  year   = {2021}
}
R2 v1 2026-06-23T02:06:24.445Z