Jaffe, Arthur MichaelMartinez II, Roberto2013-10-082013-10-082013Martinez II, Roberto. 2013. Singularities, Supersymmetry and Combinatorial Reciprocity. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:10093http://nrs.harvard.edu/urn-3:HUL.InstRepos:11151532This work illustrates a method to investigate certain smooth, codimension-two, real submanifolds of spheres of arbitrary odd dimension (with complements that fiber over the circle) using a novel supersymmetric quantum invariant. Algebraic (fibered) links, including Brieskorn-Pham homology spheres with exotic differentiable structure, are examples of said manifolds with a relative diffeomorphism-type that is determined by the corresponding (multivariate) Alexander polynomial.en-USMathematicsPhysicsThesis or Dissertation2015-06-08