Cobordism of manifolds with strong almost tangent structures

Abstract

This paper studies the unoriented cobordism classes of closed smooth manifolds whose tangent bundles admit nilpotent bundle endomorphisms. 1. Introduction. An almost tangent manifold is a smooth (differentiable of class C00) manifold M2n for which the structure group of its tangent bundle τ(M) reduces to the group of matrices of the form (# °), A e GLn(R), B G End(iΓ). The study of these manifolds is motivated by the observation that tangent manifolds have this property, i.e., if Nn is a smooth manifold and E2n is the total space of τ(N), then E2n (a tangent manifold) is an almost tangent manifold. Note that if M 2 is almost tangent, then the matrix