Hempel, John2018-12-182018-12-181984Austin, David M.. "Representations of low dimensional manifolds as branched coverings of spheres." (1984) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104682">https://hdl.handle.net/1911/104682</a>.https://hdl.handle.net/1911/104682We show that any 2- or 3-dimensional manifold is a branched covering of the sphere branched over a universal branching set. Using the associated unbranched covering, we show that there is a one-to-one correspondence between these branched coverings and pairs of permutations. In particular, this gives a means of studying manifolds. The goal of this work is to determine how much information about the manifold is readily accessible from the permutations.125 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE2318reformatted digitalThesis Math. 1984 Austin