Download E-books Complex Kleinian Groups (Progress in Mathematics) PDF

By Angel Cano

This monograph lays down the rules of the idea of complicated Kleinian teams, a newly born quarter of arithmetic whose starting place strains again to the paintings of Riemann, Poincaré, Picard and so forth. Kleinian teams are, classically, discrete teams of conformal automorphisms of the Riemann sphere, and those could be seemed too as being teams of holomorphic automorphisms of the complicated projective line CP1. whilst going into better dimensions, there's a dichotomy: may still we glance at conformal automorphisms of the n-sphere?, or should still we glance at holomorphic automorphisms of upper dimensional advanced projective areas? those theories are assorted in greater dimensions. within the first case we're speaking approximately teams of isometries of genuine hyperbolic areas, a space of arithmetic with a long-standing culture. within the moment case we're conversing approximately a space of arithmetic that also is in its adolescence, and this can be the point of interest of analysis during this monograph. This brings jointly a number of vital parts of arithmetic, as for example classical Kleinian team activities, complicated hyperbolic geometry, chrystallographic teams and the uniformization challenge for complicated manifolds.​

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