4 citations · 7 across the 11 of their papers we have counts for
11 papers
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…
State integrals for the quantized Chern-Simons invariant
Calvin McPhail-Snyder
Previous work of the author and N. Reshetikhin defines an invariant of a knot , a representation $ρ: π_{1}(S^{3} \setminus K) \to \operatorname…
A quantization of the Chern-Simons invariant of tangle exteriors
Calvin McPhail-Snyder
We define a sequence of invariants of tangles with flat connections (i.e. hyperbolic structures) on their complements. These can be interpre…
The holonomy braiding for in terms of geometric quantum dilogarithms
Calvin McPhail-Snyder, Nicolai Reshetikhin
We derive an explicit formula for the holonomy -matrix of quantum at a root of unity. We show it factorizes into a product of four quantum dilogarithms and sat…
Octahedral coordinates from the Wirtinger presentation
Calvin McPhail-Snyder
Let be a representation of a knot group (or more generally, the fundamental group of a tangle complement) into expressed in terms of the Wirti…
Surgery calculus for classical Chern-Simons theory
Calvin McPhail-Snyder
Classical -Chern-Simons theory assigns a -manifold with representation its complex volume $\…
Hyperbolic structures on link complements, octahedral decompositions, and quantum
Calvin McPhail-Snyder
Hyperbolic structures on link complements (equivalently, representations of the fundamental group into ) can be described algebraically by using th…
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 at a root of unity. These are generalized quantum invarian…
-holonomy invariants of links
Calvin McPhail-Snyder
Quantum invariants like the colored Jones polynomial are algebraic in nature but are conjectured to detect important information about the geometry of links. In this thesis we expl…
Holonomy invariants of links and nonabelian Reidemeister torsion
Calvin McPhail-Snyder
We show that the reduced -twisted Burau representation can be obtained from the quantum group for a fourth root…
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 \…