J. Brandon Coates - Honors in Mathematic
s Cwatsets and Two-Dimensional Cell Complexes


Cwatset theory is a rich theory discovered within the past two decades by undergraduates at Rose-Hulman University. Cwatsets mimic the properties of groups, and have a strong link to graph theory. This paper presents a method for constructing two-dimensional cell complexes from cwatsets. These two-dimensional cell complexes created from equivalent cwatsets under a dihedral permutation are homeomorphic. Furthermore, it is possible to calculate the Euler characteristic based solely on the cwatset used to create a two-complex and to use this invariant as a tool in classification of the two-complexes.