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The Plain Sphere Number of a Link https://arxiv.org/abs/2504.10517 #mathGT

The Plain Sphere Number of a Link

Let $L$ be a link in $S^3$. We consider the class of meridional presentations for $π_1(S^3\backslash L)$ in which the relations are witnessed by embedded two-spheres which are in plain sight in a fixed diagram of $L$. The Wirtinger presentation is a special case. We prove that the bridge number of $L$ equals the smallest number of generators of $π_1(S^3\backslash L)$ over all such presentations.

arXiv.org
April 17, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
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