Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics

The relation between Wild Topology, Hyperbolic Geometry and Fusion Algebra on the one side and the charge and coupling constants of the standard model and quantum gravity on the other is examined. The close connection found between E-(infinity) theory and the Topological theory of four manifolds as well as the theory of fundamental groups is elucidated using various classical theories and recent results due to Antoine, Wada, Alexander, Klein, Kummer, Freedman, Kaufmann, Witten, Jones and Connes. (C) 2002 Published by Elsevier Science Ltd.