Mr Edward Watts

Honours thesis

Shabat polynomials

The thesis presents some basic results from algebraic topology, including quotient spaces, homotopy and the fundamental group, and then provides an overview of the theory of covering spaces. The main theorem (that there is a bijective correspondence between Shabat polynomials and non-isomorphic plane trees) is proved by the use of covering spaces and some Riemann surface theory. Finally some calculations are presented.