3 papers
math.GT2026
Volumes of ideal hyperbolic drums
Eric Chesebro, Justin Lanier, Emma N. McQuire +3
Milnor computed the volumes of ideal hyperbolic prisms as part of an effort to construct 3-manifolds whose volumes are finite rational sums of the Lobachevsky function evaluated at…
math.GT2025
A robot that unknots knots
Connie On Yu Hui, Dionne Ibarra, Louis H. Kauffman +4
Consider a robot that remembers only the starting position and walks along a knot once on a knot diagram, switching every undercrossing it meets until it returns to the starting po…
math.GT2025
Augmented links, shadow links, and the TV volume conjecture: a geometric perspective
Dionne Ibarra, Emma N. McQuire, Jessica S. Purcell
For hyperbolic 3-manifolds, the growth rate of their Turaev-Viro invariants, evaluated at a certain root of unity, is conjectured to give the hyperbolic volume of the manifold. Thi…