Sutured manifolds and polynomial invariants from higher rank bundles

For each integer N 2, Mariño and Moore defined generalized Donaldson invariants by the methods of quantum field theory, and made predictions about the values of these invariants. Subsequently, Kronheimer gave a rigorous definition of generalized Donaldson invariants using the moduli spaces of anti-self-dual connections on hermitian vector bundles of rank N. We confirm the predictions of Mariño and Moore for simply connected elliptic surfaces without multiple fibers and certain surfaces of general type in the case that N D 3. The primary motivation is to study 3–manifold instanton Floer homologies which are defined by higher rank bundles. In particular, the computation of the generalized Donaldson invariants is exploited to define a Floer homology theory for sutured 3–manifolds.