On toroidal knots, chirality, and molecules
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The inspiration for this thesis came from two sources: the book When topology meets chemistry: a topological look at molecular chirality, by Erica Flapan , which discusses topologically interesting molecules; and the paper All toroidal embeddings of polyhedral graphs in 3-space are chiral, by T. Castle et al., which proves that toroidal embeddings of polyhedra are chiral. Their proof is examined in detail. A possible application of this work, as discussed by the team, would be in molecules which have the structure of a toroidal polyhedral embedding. Various methods of seeking such an example are attempted and discussed.