Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids

Judson Kuhrman

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arXiv · 2605.14996

Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids

Judson Kuhrman

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Abstract

We establish a formula expressing Miyazawa's 2-knot invariant $|\mathrm{deg}|$ in terms of the Lefschetz number of a map on ordinary (i.e., not real) monopole Floer homology. As an application, we deduce that $|\mathrm{deg}|=1$ for any 2-knot in $S^4$ which has a punctured $L$-space as a Seifert solid. In the course of the proof of the main theorem, we show how Francesco Lin's construction of monopole Floer homology with $\operatorname{Pin}(2)$-equivariant perturbations can be made to work with integer coefficients.

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Judson Kuhrman. 2026-05-14. Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids. https://arxiv.org/abs/2605.14996

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