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The Kauffman Bracket Skein Module Of The Quaternionic Manifold, John Michael Harris

LSU Doctoral Dissertations

In this work, we study the structure of the Kauffman bracket skein module of the quaternionic manifold over the field of rational functions. We begin with a brief survey of manifolds whose Kauffman bracket skein modules are known, and proceed in Chapter 2 by recalling the facts from Temperley-Lieb recoupling theory that we use in the proofs. In Chapter 3, using recoupling theory and with Mathematica's assistance, we index an infinite presentation of the skein module, and conjecture that it is five-dimensional. In Chapter 4, using a new set of relations, we prove that the skein module is indeed spanned …