Some lower bounds for the Kirby-Thompson invariant

Nobutaka Asano; Hironobu Naoe; Masaki Ogawa

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arXiv · 2302.07447

Some lower bounds for the Kirby-Thompson invariant

Nobutaka Asano·Hironobu Naoe·Masaki Ogawa

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Abstract

Kirby and Thompson introduced a non-negative integer-valued invariant, called the Kirby-Thompson invariant, of a $4$-manifold using trisections. In this paper, we give some lower bounds for the Kirby-Thompson invariant of certain $4$-manifolds. As an application, we determine the Kirby-Thompson invariant of the spin of $L(2,1)$, which is the first example of a $4$-manifold with non-trivial Kirby-Thompson invariant. We also show that there exist $4$-manifolds with arbitrarily large Kirby-Thompson invariant.

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Nobutaka Asano, Hironobu Naoe, Masaki Ogawa. 2023-02-15. Some lower bounds for the Kirby-Thompson invariant. https://arxiv.org/abs/2302.07447

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