If f : X → S is a submersive fibration of complex analytic manifolds, given a point x ∈ X, there is an exact sequence of fundamental groups 0 → π 1 F q , ρ) is an isomorphism, this action defines the cohomology of the fibers as a local system over the base, resp. a Galois action on the cohomology of ρ over X × Fq ¯ F q. A good analog in algebraic geometry of the topological fundamental group on...

If f : X → S is a fibration of complex connected analytic manifolds, given a point x ∈ X, there is an exact sequence of fundamental groups 0 → π 1 F q , ρ) is an isomorphism, this action defines the coho-mology of the fibers as a local system over the base, resp. a Galois action on the cohomology of ρ over X × Fq ¯ F q. A good analog in algebraic geometry of the topological fundamental group on...

Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain frequently reflects local properties which are missed by the usual arcwise group iri(X, Xo). We obtain a perfect Galois theory of covering...

This paper investigates fundamental theorems of regular variation (Uniform Convergence, Representation, and Characterization Theorems) some of which, in the classical setting of regular variation in R, rely in an essential way on the additive semi-group of natural numbers N (e.g. de Bruijn’s Representation Theorem for regularly varying functions). Other such results include Goldie’s direct proo...

A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the cyclic properties (S homotopy) of the topological manifold Q = 2T 3 ⊕ 3S × S which has 23 intrinsic degrees of freedom, discrete Z3 and Z2×Z3 internal group...

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional cohomology classes associated with certain irreducible representations of this group. The proofs are based on Topological Quantum Field Theory. AMS Subject classific...

We consider some smooth maps on a bouquet of circles. For these maps we can compute the number of fixed points, the existence of periodic points and an exact formula for topological entropy. We use Lefschetz fixed point theory and actions of our maps on both the fundamental group and the first homology group.