Cohomological Constructions of Regular Cyclic Coverings of the Platonic Maps

AbstractIn we described the regular maps and hypermaps which are cyclic coverings of the Platonic maps, branched over the face centers, vertices or midpoints of edges. Here we determine cochains by which these coverings can be explicitly constructed

Singularities, Supersymmetry and Combinatorial Reciprocity

This 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.Engineering and Applied Science