Victor Goryunov (University of Liverpool)
The talk is about a classification of order $1$ invariants of maps between $3$-manifolds whose increments in generic homotopies are defined entirely by diffeomorphism types of local bifurcations.
I will mainly concentrate on the oriented situation. In this case the space of integer invariants has rank $7$ for any source and target, and I will give a geometric interpretation of its basis. The $\mod 2$ setting, with $\mathbb R^3$ as the target, adds another $4$ linearly independent invariants, one of which combines the self-linking of the cuspidal edge of the critical value set with the number of connected components of the edge.