Aarhus University Seal / Aarhus Universitets segl

4-manifolds, and intersection forms with local coefficients

Kim Froyshov
(University of Zürich)
Topology Seminar
Wednesday, 3 February, 2010, at 16:15-17:15, in Aud. D3 (1531-215)
Abstract:
Let X be a closed, oriented, smooth 4-manifold. For every element v of H1(X;Z/2) one can associate a bundle L of infinite cyclic groups over X (or more precisely: an isomorphism class of such bundles). Using singular (co)homology with coefficients in this bundle one can define in the usual way an "intersection form" Q_v on H_2(X;L) / torsion, and this form is unimodular. In the 1980's Donaldson proved, using instanton moduli spaces, that if the usual intersection form Q_0 is definite then it must be diagonal. Until recently, little seemed to be known about Q_v when v is non-zero. In this talk I will show that there are in fact constraints on the definite Q_v. The proof introduces some new twists to the ideas of Donaldson.
Organised by: CTQM/QGM
Contact person: Jørgen Ellegaard Andersen