Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project B2

## Combinatorial and topological structure of aperiodic tilings

Principal Investigator(s) Other Investigators

## Summary:

Combinatorial aspects of periodic and aperiodic tilings are investigated, with special emphasis on generalised symmetries and topological invariants. Of particular interest are crystallographically relevant sublattice structures and their generalisations to $\mathbb{Z}$-modules as well as the calculation and the geometric understanding of cohomology and K-groups for tiling spaces.

This project continues the successful work of the project Combinatorial and geometric structure of aperiodic tilings under the direction of Christoph Richard and Michael Baake.

## Recent Preprints:

 13009 Similar sublattices of planar lattices PDF | PS.GZ 13008 The coincidence problem for shifted lattices and multilattices PDF | PS.GZ 13007 CSLs of the root lattice $\mathbf{A_4}$ PDF | PS.GZ 12150 Multiplicativity in the theory of coincidence site lattices PDF | PS.GZ 12149 Well-rounded sublattices and coincidence site lattices PDF | PS.GZ 12148 Colourings of lattices and coincidence site lattices PDF | PS.GZ 12147 Coincidence isometries of a shifted square lattice PDF | PS.GZ 12128 Examples of substitution systems and their factors PDF | PS.GZ 12116 Substitution rules and topological properties of the Robinson tilings PDF | PS.GZ 12115 Hexagonal inflation tilings and planar monotiles PDF | PS.GZ