Cobordism group of fold maps of oriented 3-manifolds into the plane

Abstract

Abstract We give a Pontryagin-Thom type construction for Stein factorizations of fold maps of 3-manifolds into the plane. As an application, we compute the cobordism group of Stein factorizations of fold maps of oriented 3-manifolds into the plane and the oriented cobordism group of fold maps of 3-manifolds into the plane. It turns out that these two groups are isomorphic to Z 2 ⊕ Z 2. We have the analogous results about bordism groups as well.