Hypersingular integral equations, Kaehler manifolds and Thurston mirroring effect in ε (∞) Cantorian spacetime

In this work starting from some earlier results on hypersingular integral equations and analyzing a more realistic model of gravitational waveguides on a Cantorian spacetime we obtain a description of our Universe according to Kaehler manifold in the context of El Naschie's ε (∞) Cantorian space-time. In particular, we consider filamentary and planar large scale structures as possible refraction channels for electromagnetic radiation coming from cosmological structures. From this vision the Universe appears like a large self-similar adaptive mirrors set. This is made evident through numerical simulations. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected to the large scale structure of a finite and not so large Universe