By Pol Vanhaecke

This booklet treats the final idea of Poisson buildings and integrable platforms on affine kinds in a scientific manner. targeted realization is interested in algebraic thoroughly integrable structures. a number of integrable platforms are developed and studied intimately and some functions of integrable platforms to algebraic geometry are labored out. within the moment variation a number of the suggestions in Poisson geometry are clarified by way of introducting Poisson cohomology; the Mumford platforms are made from the algebra of pseudo-differential operators, which clarifies their foundation; a brand new rationalization of the multi Hamiltonian constitution of the Mumford structures is given by means of utilizing the loop algebra of sl(2); and at last Goedesic move on SO(4) is further to demonstrate the linearizatin algorith and to offer one other program of integrable structures to algebraic geometry.

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