By Angel Cano,Juan Pablo Navarrete,Seade Kuri José Antonio

This monograph lays down the principles of the idea of complicated Kleinian teams, a newly born quarter of arithmetic whose beginning lines 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 should be appeared too as being teams of holomorphic automorphisms of the complicated projective line CP1. while going into better dimensions, there's a dichotomy: may still we glance at conformal automorphisms of the n-sphere?, or may 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 conversing approximately teams of isometries of actual hyperbolic areas, a space of arithmetic with a long-standing culture. within the moment case we're speaking approximately a space of arithmetic that also is in its adolescence, and this is often the focal point of analysis during this monograph. This brings jointly a number of vital components of arithmetic, as for example classical Kleinian staff activities, complicated hyperbolic geometry, chrystallographic teams and the uniformization challenge for advanced manifolds.​

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