Symplectic reduction on pseudomanifolds
Tshilombo, Mukinayi Hermenegilde
The dissertation consists of symplectic reduction on a Fr¨olicher space which is locally diffeomorphic to an Euclidean Fr¨olicher subspaces of Rn of constant dimension equal to n. Such a space is called a Fr¨olicher pseudomanifold or simply a pseudomanifold. The symplectic reduction under consideration in this work is an extension of the Marsden-Weinstein quotient (the reduced space) well-known for the finite-dimensional smooth manifold. Starting with a proper and free action of a Fr¨olicher-Lie-group on a finite constant dimensional pseudomanifold, we study the smooth structure induced on a small subspace of the orbit space. Aside the algebraic and geometric study of these new objects(pseudomanifolds), the work contains their topological fundamentals and symplectic structures, as well as an introduction to the geometric control theory.