We define two classes of topological infinite degree covering maps modeled on two families of transcendental holomorphic maps. The first, which we call exponential maps of type (p, q), are branched covers and is modeled on transcendental entire maps of the form Pe, where P and Q are polynomials of degrees p and q. The second is the class of universal covering maps from the plane to the sphere w...

A natural problem in the theory of 3-manifolds is the question of whether two 3-manifolds are homeomorphic or not. The aim of this paper is to study this problem for the class of closed Haken manifolds using degree one maps. To this purpose we introduce an invariant τ(N) = (Vol(N), ‖N‖) where ‖N‖ denotes the Gromov simplicial volume of N and Vol(N) is a 2-dimensional simplicial volume which mea...

I give a proof of the Borsuk-Ulam Theorem which I claim is a simplified version of the proof given in Bredon [1], using chain complexes explicitly rather than homology. Of course this is a matter of taste, and the mathematical content is identical, but in my opinion this proof highlights precisely where and how the contradiction arises. 1 Statements and Preliminaries Theorem 1.1 (Borsuk-Ulam). ...

We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of “typical” covering maps, and use graph Galois theory to “symmetrize” the conjecture. The conjecture is then related to certain kernel of a morphism of sheaves, and is implied provided these kernels are co-acyclic in the covering cohomology theory. This allows us t...

We prove that the canonical Thurston obstruction for a sub-hyperbolic semi-rational branched covering exists if the branched covering is not CLH-equivalent to a rational map.

We demonstrate that the question whether or not a given topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.

Given a sub-hyperbolic semi-rational branched covering which is not CLH-equivalent a rational map, it must have the non-empty canonical Thurston obstruction. By using this canonical Thurston obstruction, we decompose this dynamical system in this paper into several sub-dynamical systems. Each of these subdynamical systems is either a post-critically finite type branched covering or a sub-hyperb...

heat stress is a major environmental stress limiting wheat productivity in most cereal growing areas of the world. in order to map and characterize quantitative trait loci controlling heat tolerance, 144 recombinant inbred lines deriving from the cross of kauz and mtrwa116 were assessed in a greenhouse and growth chamber at 35°c. one hundred and sixty six ssr and 3 aflp markers were used to...