English

Some lower bounds for the Kirby-Thompson invariant

Geometric Topology 2023-02-28 v2

Abstract

Kirby and Thompson introduced a non-negative integer-valued invariant, called the Kirby-Thompson invariant, of a 44-manifold using trisections. In this paper, we give some lower bounds for the Kirby-Thompson invariant of certain 44-manifolds. As an application, we determine the Kirby-Thompson invariant of the spin of L(2,1)L(2,1), which is the first example of a 44-manifold with non-trivial Kirby-Thompson invariant. We also show that there exist 44-manifolds with arbitrarily large Kirby-Thompson invariant.

Keywords

Cite

@article{arxiv.2302.07447,
  title  = {Some lower bounds for the Kirby-Thompson invariant},
  author = {Nobutaka Asano and Hironobu Naoe and Masaki Ogawa},
  journal= {arXiv preprint arXiv:2302.07447},
  year   = {2023}
}

Comments

20 pages, 6 figures

R2 v1 2026-06-28T08:40:25.439Z