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)

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