Winding number $m$ and $-m$ patterns acting on concordance

Allison N. Miller

Winding number $m$ and $-m$ patterns acting on concordance

Geometric Topology 2017-12-20 v2

Authors: Allison N. Miller

Abstract

We prove that for any winding number $m>0$ pattern $P$ and winding number $-m$ pattern $Q$ , there exist knots $K$ such that the minimal genus of a cobordism between $P(K)$ and $Q(K)$ is arbitrarily large. This answers a question posed by Cochran-Harvey [CH17] and generalizes a result of Kim-Livingston [KL05].

Keywords

knot theory

Cite

@article{arxiv.1712.05719,
  title  = {Winding number $m$ and $-m$ patterns acting on concordance},
  author = {Allison N. Miller},
  journal= {arXiv preprint arXiv:1712.05719},
  year   = {2017}
}

Comments

9 pages, 1 figure. v2 has correct version of Figure 1

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