Cohomology in one-dimensional substitution tiling spaces

By Marcy Barge, B. Diamond. 2007

51 citations recorded by the source corpus.

Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which "forces its border." One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomorphism induced by inflation and substitution on the cohomology of the complex. For one-dimensional substitution tiling spaces, we describe a modification of the Anderson-Putnam complex on collared tiles that allows for easier computation and provides a means of identifying certain special features of the tiling space with particular elements of the cohomology.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/11135984ff864aaf9545dfcdf5db57523f1f185e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Anne Siegel
2. Val'erie Berth'e
3. Marcy Barge
4. J.-Y. Lee
5. Shigeki Akiyama
6. Jörg M. Thuswaldner
7. Wolfgang Steiner
8. Hui Rao

In Discrete Mathematics and Combinatorics

1. Anne Siegel
2. Val'erie Berth'e
3. Shigeki Akiyama

In Materials Chemistry

1. Marcy Barge
2. Val'erie Berth'e
3. Anne Siegel
4. J.-Y. Lee
5. Shigeki Akiyama

Citations in the corpus

• On the Pisot Substitution Conjecture (2015, background): “The expansion λ is an eigenvalue of this isomorphism so the dimension of H(1)(Ω) is at least the algebraic degree d of λ ([26]).”