Research Proposal

Justin T Miller

This goal of this research project is to create a Mathematica package that can compute the homology and cohomology groups of simplicial complexes. The research will begin with a study of those parts of algebraic topology necessary to understand the concepts of homology, cohomology, and a simplicial complex. The next part of the research will involve leaning how to use Mathematica, and designing the data structures and algorithms required to compute the homology and cohomology groups, and the cup product. Once the Mathematica package has been created, a short paper will be written about the package and submitted to the Mathematica Journal. Applications of the project, including knot theory, will also be considered.