Speaker
Description
Branched coverings can be seen a way to represent a ''complicated manifolds'' M in terms of
- a ''simpler'' manifold N (the target of the branched coverig),
-a codimension two subcomplex K in N (the branch set),
-a representation of the fundamental group of the complement of K into a permutation group (the monodromy).
By a classical result of Alexander, every piecewise linear manifold admits a branched covering onto the sphere. On the other hand, given an arbitraty manifold N, its topology might restrict the set of manifolds arising as its branched coverings.
I will talk about a recent joint work with Riccardo Piergallini and Daniele Zuddas, where we prove that, given a closed connected 4-manifold N with no 1- and 3-handles, there is a simple d-fold branched covering from M to N if and only if d times the intersection lattice of N isometrically embeds into the intersection lattice of M. We also give conditions on the degree and on the regularity of the branch set.