Tiling spaces, inverse limits and cohomology

Speaker(s)

Lorenzo Sadun

Affiliation

University of Texas at Austin

Language of the talk

English

Date

May 21, 2025, 10:15 a.m.

Room

room 4070

Seminar

Seminar Algebraic Topology

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Tiling dynamical systems are of both topological and dynamical interest. The set of tilings
with a given local structure is a ``matchbox manifold'', locally modeled on the product of a Cantor
set with Euclidean space. Globally, these spaces can be viewed as inverse limits of branched
manifolds. This inverse limit structure allows us to compute topological invariants, such as the Cech
cohomology. The Cech cohomology in turn parametrizes properties of individual tilings, relating
algebraic topology to local geometry. As an application, we will use this circle of ideas to
understand why all versions of the recently discovered ``Hat'' tilings have essentially the same
dynamical properties.

 

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