3 papers
math.AT2026
Covers of Tiling Spaces
Franz Gähler, Jianlong Liu, Lorenzo Sadun
We study the ways that one tiling space can be a finite regular cover of another. We classify all of the finite regular covers of a tiling space via its structure as an inverse lim…
math.DS2024
On the long-range order of the Spectre tilings
Michael Baake, Franz Gähler, Jan Mazáč +1
The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dy…
math.AT2016
Lecture Notes on Differential Forms
Lorenzo Sadun
This is a series of lecture notes, with embedded problems, aimed at students studying differential topology. Many revered texts, such as Spivak's "Calculus on Manifolds" and Guille…