El Naschie E-Infinity Cantorian space-time, Fantappiè’s group and applications in cosmology

In this paper starting from the Fantappie group we will consider its properties in connection with E-infinity Cantorian space-time. The cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible. In particular, if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection, the two models become compatible. In the end we will see the effects of the projective fractal geometry also on the galactic and extra-galactic dynamics; in particular, we analyze the effects of Fantappie's transformation on gravitational lenses and we will see that the gravitational lensing effects could be a good tool to verify this theory.