Abstract

We present here a method for computing the homology of a substitution tiling space. There is a well established cohomology theory that uses simple matrix computations to determine if two tiling spaces are dierent. We will show how to compute Putnam's homology groups for these spaces using simple linear algebra. We construct a Markov Partition based on the substitution rules, and exploit the properties of this partition as a shift of finite type to construct algebraic invariants for the tiling space. These invariants form a chain complex, of which we can compute the homology. In our examples we will demonstrate an interesting duality between the cohomology and homology of these spaces. This leads to a conjecture relating the two theories to each other and we present the reasoning behind the conjecture.

Advisor

Brian Martensen

First Committee Member

Cia Chi Tung

Second Committee Member

Karla Lassonde

Date of Degree

2011

Language

english

Document Type

Thesis

Degree

Master of Science (MS)

Department

Mathematics and Statistics

College

Science, Engineering and Technology

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

Included in

Mathematics Commons

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