Calvin McPhail-Snyder

collaborators

6 papers

math.QA2026

Zesting and the relative complexity of Reshetikhin-Turaev invariants

Colleen Delaney, Calvin McPhail-Snyder

We show that the computational complexity of Reshetikhin-Turaev invariants of simply colored links is preserved when their underlying ribbon fusion categories are related by the ze…

math.GT2026

State integrals for the quantized $SL_{2} (C)$ Chern-Simons invariant

Calvin McPhail-Snyder

Previous work of the author and N. Reshetikhin defines an invariant $Z_{N}^{I ¨} (K, I ¨ , I^¼)$ of a knot $K$ , a representation $Ï: Ï_{1}(S^{3} \setminus K) \to \operato…

math.QA2026

A quantization of the $SL_{2} (C)$ Chern-Simons invariant of tangle exteriors

Calvin McPhail-Snyder

We define a sequence of invariants $Z_{N}^{I ¨} $ of tangles with flat $sl_{2}$ connections (i.e. hyperbolic structures) on their complements. These can be interpr…

math.QA2026

The holonomy braiding for $U_{I^} ¾ (sl_{2})$ in terms of geometric quantum dilogarithms

Calvin McPhail-Snyder, Nicolai Reshetikhin

We derive an explicit formula for the holonomy $R$ -matrix of quantum $sl_{2}$ at a root of unity. We show it factorizes into a product of four quantum dilogarithms and sat…

math.GT2026

Hyperbolic structures on link complements, octahedral decompositions, and quantum $sl_{2}$

Calvin McPhail-Snyder

Hyperbolic structures on link complements (equivalently, representations of the fundamental group into $SL_{2} (C)$ ) can be described algebraically by using th…

math.GT2025

Octahedral coordinates from the Wirtinger presentation

Calvin McPhail-Snyder

Let $I ¨ $ be a representation of a knot group (or more generally, the fundamental group of a tangle complement) into $SL_{2} (C)$ expressed in terms of the Wirt…

Zesting and the relative complexity of Reshetikhin-Turaev invariants

State integrals for the quantized SL2​(C) Chern-Simons invariant

A quantization of the SL2​(C) Chern-Simons invariant of tangle exteriors

The holonomy braiding for UI^​¾(sl2​) in terms of geometric quantum dilogarithms

Hyperbolic structures on link complements, octahedral decompositions, and quantum sl2​

Octahedral coordinates from the Wirtinger presentation

State integrals for the quantized $SL_{2} (C)$ Chern-Simons invariant

A quantization of the $SL_{2} (C)$ Chern-Simons invariant of tangle exteriors

The holonomy braiding for $U_{I^} ¾ (sl_{2})$ in terms of geometric quantum dilogarithms

Hyperbolic structures on link complements, octahedral decompositions, and quantum $sl_{2}$