Publications [#383423] of Calvin McPhail-Snyder

Papers Published

1. McPhail-Snyder, C, Octahedral coordinates from the Wirtinger presentation, Geometriae Dedicata, vol. 219 no. 4 (August, 2025) [doi]
   (last updated on 2026/01/17)

   Abstract:
   Let ρ be a representation of a knot group (or more generally, the fundamental group of a tangle complement) into SL2(C) expressed in terms of the Wirtinger generators of a diagram D. This diagram also determines an ideal triangulation of the complement called the octahedral decomposition. ρ induces a hyperbolic structure on the complement of D, and in this note we give a direct algebraic formula for the geometric parameters of the octahedral decomposition induced by this structure. Our formula gives a new, explicit criterion for whether ρ occurs as a critical point of the diagram’s Neumann–Zagier–Yokota potential function.