Homotopy theory and derived categories

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I will work on two topics: configuration spaces and t-structures. A manifold M can be thought of as a space of possible locations of an object or as the possible states of a mechanical system. For example M=R3, Euclidean three space is the three dimensional space we live in. The configuration space on k points F(M,k) consists of k particles in the manifold that are not allowed to collide. So they are sequences of points no two of which can be the same. For example it could be the states of a robot with many arms. Again if we think of Euclidean three space, then F(R3,k) could be thought of as the possible states of a universe with k planets in it. I am particularly interested in the relation between M and F(M,k), am working on a mathematical way of getting information about F(M,k) from information about M.