Grant: Discovery Grants Program - Individual

Our program involves applying methods from homotopy theory to goemetric problems. One way to do this is by studying the complement M\P of a polyhedron P in a manifold M. An example of a manifold would be the possible positions of a mechanical system such as the planets in the solar system. The polyhedron would then correspond to unallowed positions, such as two planets being in the same location. The complement M\P would then correspond to allowable positions. We use algebraic invariants to give us information about this complement. In the case of a mechanical system, these invariants can control the behaviour of the system.