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

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

This monograph lays down the principles of the speculation of complicated Kleinian teams, a newly born sector of arithmetic whose beginning 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 seemed too as being teams of holomorphic automorphisms of the complicated projective line CP1. while going into larger 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 complicated projective areas? those theories are various in greater dimensions. within the first case we're conversing 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 focal point of research during this monograph. This brings jointly a number of very important components of arithmetic, as for example classical Kleinian workforce activities, advanced hyperbolic geometry, chrystallographic teams and the uniformization challenge for advanced manifolds.​

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