Evaluation of Euler number of complex Grassmann manifold G(k,N) via Mathai-Quillen formalism

In this paper, we provide a recipe for computing Euler number of Grassmann manifold G(k, N) by using Mathai-Quillen formalism (MQ formalism) [9] and Atiyah-Jeffrey construc-tion [1]. 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).