Tyrone Cutler

activity

20192026

collaborators

6 papers

math.AT2026

Inductive construction of path homology chains and the structure of $Ω_{3} (G; R)$

Matthew Burfitt, Tyrone Cutler

Path homology plays a central role in digraph topology and GLMY theory more generally. Unfortunately, the computation of the path homology of a digraph $G$ is a two-step process, a…

math.AT2026

On the homotopy types of $4$ -dimensional toric orbifolds

Tyrone Cutler, Tseleung So

The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological r…

math.AT2024

Inductive construction of path homology chains

Matthew Burfitt, Tyrone Cutler

Path homology plays a central role in digraph topology and GLMY theory more general. Unfortunately, the computation of the path homology of a digraph $G$ is a two-step process, and…

math.AT2023

Suspension splittings of 5-dimensional Poincaré duality complexes and their applications

Steven Amelotte, Tyrone Cutler, Tseleung So

Let $X$ be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free $H_{1} (X; Z)$ . We show that $Σ X$ is homotopy equivalent to a wedge of recognisabl…

math.AT2021

The homotopy type of a once-suspended 6-manifold and its applications

Tyrone Cutler, Tseleung So

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $Σ M$ in terms of spheres, Moore spaces and other rec…

math.AT2019

The Homotopy Types of $S U (4)$ -Gauge Groups

Tyrone Cutler, Stephen Theriault

Let $G_{k}$ be the gauge group of the principal $S U (4)$ -bundle over $S^{4}$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$ -local…