Multiframings of 3-manifolds

Abstract

We investigate multiframings of a closed oriented 3-manifold. We show that multiframings give a geometric realization of the tensor product of the homotopy set of framings and [Formula: see text]. We prove that the Hirzebruch defect defines a bijection from the homotopy set of multiframings to [Formula: see text] for any connected closed oriented 3-manifold, and we prove that any multiframing defined near the boundary of a compact oriented 3-manifold extends to the bounded manifold.