An Algorithmic Search for Knots Bounding M\"obius Bands in $B^4$

Daniel Lee; Joshua M. Sabloff

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arXiv · 2607.23582

An Algorithmic Search for Knots Bounding M\"obius Bands in $B^4$

Daniel Lee·Joshua M. Sabloff

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Abstract

This study examines the smooth non-orientable $4$-genus of knots using a large-scale computational search. Knot invariant obstructions were computed, and existing computational algorithms were extended to identify prime knots in $S^3$ of crossing number at most $14$ that bound M\"obius bands in $B^4$. The findings significantly expand the known examples of knots of non-orientable $4$-genus equal to $1$ and contribute new data relevant to the study of the non-orientable $4$-genus.

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Daniel Lee, Joshua M. Sabloff. 2026-07-26. An Algorithmic Search for Knots Bounding M\"obius Bands in $B^4$. https://arxiv.org/abs/2607.23582

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