Mod2 local invariants of maps between 3-manifolds

Abstract

This paper refers to the work [V. Goryunov, Local invariants of maps between 3-manifolds, J. Topology 6 (2013) 757–776] on local invariants of maps between 3-manifolds. It is assumed that the manifolds have no boundary, and that the source is compact. In the case when the source and the target are oriented, Goryunov proved that every local order one invariant with integer values can be written as a linear combination of seven basic invariants, and gave a geometrical interpretation for them. When the target is the oriented [Formula: see text], there are further four basic mod2 invariants. One of the mod2 invariants has been provided with a topological interpretation, in terms of the number of components and of the self-linking of a framed link constructed from the cuspidal edge. Here, we show that two further independent linear combinations of the mod2 invariants have a topological interpretation, involving the self-linking number of two curves defined by all irregular points of the critical value set of a generic map from an oriented closed 3-manifold to [Formula: see text].