Kauffman’s clock theorem and its generalisation to more complicated structures and surfaces

The thesis aims to generalise Kauffman’s clock theorem as much as possible. We start with a universe, which is a graph where every vertex has four edges incident to it. Putting a marker at each vertex such that every face has exactly one marker except two fixed faces produces a state. The theorem says that the set of states is a lattice under transpositions. We then generalise a universe to a multiverse and prove that the theorem still holds for a multiverse embedded on a surface with more than one boundary component and non-zero genus.