English

Pants distances of knotted surfaces in 4-manifolds

Geometric Topology 2023-07-27 v1

Abstract

We define a pants distance for knotted surfaces in 4-manifolds which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine that if the distance computed on a given diagram does not surpass a theoretical bound in terms of the multisection genus, then the (4-manifold, surface) pair has a simple topology. Furthermore, we calculate the exact values of our invariants for many new examples such as the spun lens spaces. We provide a characterization of genus two quadrisections with distance at most six.

Keywords

Cite

@article{arxiv.2307.13874,
  title  = {Pants distances of knotted surfaces in 4-manifolds},
  author = {Román Aranda and Sarah Blackwell and Devashi Gulati and Homayun Karimi and Geunyoung Kim and Nicholas Paul Meyer and Puttipong Pongtanapaisan},
  journal= {arXiv preprint arXiv:2307.13874},
  year   = {2023}
}