By Pol Vanhaecke

This e-book treats the final concept of Poisson buildings and integrable platforms on affine kinds in a scientific manner. specific cognizance is interested in algebraic thoroughly integrable platforms. numerous integrable platforms are developed and studied intimately and some purposes of integrable platforms to algebraic geometry are labored out. within the moment variation many of the ideas in Poisson geometry are clarified via introducting Poisson cohomology; the Mumford structures are made out of the algebra of pseudo-differential operators, which clarifies their starting place; a brand new clarification 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 circulation on SO(4) is further to demonstrate the linearizatin algorith and to provide one other program of integrable platforms to algebraic geometry.

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