3 papers
math.GT2025
Generalised Kauffman Clock Theorems
Nguyen Thanh Tung Le, Daniel V. Mathews
Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem,…
math.GT2025
Quaternionic spinors and horospheres in 4-dimensional hyperbolic geometry
Daniel V. Mathews, Varsha
We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski…
math.GT2024
From spinors to horospheres: a geometric tour
Daniel V. Mathews, Varsha
This article is an exposition and elaboration of recent work of the first author on spinors and horospheres. It presents the main results in detail, and includes numerous subsidiar…