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math.GT2025
The 3D index and Dehn filling
Daniele Celoria, Craig D. Hodgson, J. Hyam Rubinstein
We provide a rigorous proof of the Gang-Yonekura formula describing the transformation of the 3D index under Dehn filling a cusp in an orientable 3-manifold. The 3D index, original…
math.MG2025
Compression Maps Between Polytopes
José Ayala, David Kirszenblat, J. Hyam Rubinstein
A shape of a combinatorial polytope is a convex embedding into Euclidean space. We provide necessary and sufficient conditions for a piecewise linear map between two shapes of the…