Complex Kleinian Groups: 303 (Progress in Mathematics) by Angel Cano,Juan Pablo Navarrete,Seade Kuri José Antonio

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

This monograph lays down the rules of the speculation of advanced Kleinian teams, a newly born zone of arithmetic whose foundation 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 will be appeared too as being teams of holomorphic automorphisms of the advanced projective line CP1. whilst 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 complicated projective areas? those theories are various 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 youth, and this is often the focal point of research during this monograph. This brings jointly numerous very important components of arithmetic, as for example classical Kleinian crew activities, advanced hyperbolic geometry, chrystallographic teams and the uniformization challenge for advanced manifolds.​

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