Evaluation of Euler Number of Complex Grassmann Manifold G(k, N) via Mathai-Quillen Formalism

Abstract: In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k,N) by using Mathai-Quillen formalism (MQ formalism) and Atiyah-Jeffrey construction. Especially, we construct path-integral representation of Euler number of G(k,N). Our model corresponds to a finite dimensional toy-model of topological Yang-Mills theory which motivated Atiyah-Jeffrey construction. As a by-product, we construct free fermion realization of cohomology ring of G(k,N).