How to make a triangulation of $S^3$ polytopal
How to make a triangulation of $S^3$ polytopal
We introduce a numerical isomorphism invariant $p(\mathcal {T})$ for any triangulation $\mathcal {T}$ of $S^3$. Although its definition is purely topological (inspired by the bridge number of knots), $p(\mathcal {T})$ reflects the geometric properties of $\mathcal {T}$. Specifically, if $\mathcal {T}$ is polytopal or shellable, then $p(\mathcal {T})$ is âsmallâ …