On the noncommutative geometry of tilings
Antoine Julien, Johannes Kellendonk, Jean Savinien
TL;DR
This paper reviews how noncommutative geometry tools are applied to study the topology, dynamics, and combinatorics of aperiodic tilings, providing a comprehensive overview of recent mathematical advances in this area.
Contribution
It synthesizes recent results on aperiodic tilings using noncommutative geometry, highlighting new insights into their mathematical structure.
Findings
Topological classification of aperiodic tilings
Dynamical systems associated with tilings analyzed
Combinatorial properties of tilings elucidated
Abstract
This is a chapter in an incoming book on aperiodic order. We review results about the topology, the dynamics, and the combinatorics of aperiodically ordered tilings obtained with the tools of noncommutative geometry.
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Taxonomy
TopicsCellular Automata and Applications · Quasicrystal Structures and Properties · Coding theory and cryptography