Abstract: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 limit space. If the
tiling space $\Omega$ can be written as an inverse limit
$\varprojlim \Gamma_n$, then the étale fundamental group of $\Omega$,
which is defined via a limit of covers, is isomorphic to the inverse
limit $\hat \pi_1(\Omega) := \varprojlim \hat \pi_1(\Gamma_n)$ of the
profinite completions of the fundamental groups
$\pi_1(\Gamma_n)$. This isomorphism allows us to construct all
covers of tiling spaces and to use those covers to distinguish
spaces that have identical cohomology groups.
From: Franz Gähler [view email]
[v1]
Fri, 12 Jun 2026 08:58:42 UTC (45 KB)
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