# nLab noncommutative topology of quasiperiodicity

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

Quasi-periodic geometries such as Penrose tilings and quasicrystals tend to admit useful descriptions by noncommutative topology/noncommutative geometry.

## References

### For Penrose tilings

Noncommutative topology of Penrose tilings:

### For quasicrystals

Discussion of the noncommutative topology/KK-theory of the Brillouin zone of quasi-crystals in the spirit of the K-theory classification of topological phases of matter:

• Jean Bellissard, The Noncommutative Geometry of Aperiodic Solids, in: Geometric and Topological Methods for Quantum Field Theory, pp. 86-156 (2003) (pdf, doi:10.1142/9789812705068_0002)

• Fonger Ypma, Quasicrystals, $C^\ast$-algebras and K-theory, 2005 (pdf)

• Ian F. Putnam, Non-commutative methods for the K-theory of $C^\ast$-algebras of aperiodic patterns from cut-and-project systems, Commun. Math. Phys. 294, 703–729 (2010) (pdf, doi:10.1007/s00220-009-0968-0)

Created on May 14, 2021 at 12:40:31. See the history of this page for a list of all contributions to it.