Calvin McPhail-Snyder

activity

20182026

collaborators

Showing math.GTShow all

5 papers · 1 filter

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 $Z_{N}^{ψ} (K, ρ, μ)$ of a knot $K$ , a representation $ρ: π_{1}(S^{3} \setminus K) \to \operatorname…

math.GT2024

Octahedral coordinates from the Wirtinger presentation

Calvin McPhail-Snyder

Let $ρ$ 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 Wirti…

math.GT2022

Surgery calculus for classical $SL_{2} (C)$ Chern-Simons theory

Calvin McPhail-Snyder

Classical $SL_{2} (C)$ -Chern-Simons theory assigns a $3$ -manifold $M$ with representation $ρ : π_{1} (M) \to SL_{2} (C)$ its complex volume $\…

math.GT2021

Kashaev--Reshetikhin Invariants of Links

Kai-Chieh Chen, Calvin McPhail-Snyder, Scott Morrison +1

Kashaev and Reshetikhin previously described a way to define holonomy invariants of knots using quantum $sl_{2}$ at a root of unity. These are generalized quantum invarian…

math.GT2018

Planar diagrams for local invariants of graphs in surfaces

Calvin McPhail-Snyder, Kyle A. Miller

In order to apply quantum topology methods to nonplanar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. These \…

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

Octahedral coordinates from the Wirtinger presentation

Surgery calculus for classical SL2​(C) Chern-Simons theory

Kashaev--Reshetikhin Invariants of Links

Planar diagrams for local invariants of graphs in surfaces

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

Surgery calculus for classical $SL_{2} (C)$ Chern-Simons theory