Hyperbolic four-manifolds with vanishing Seiberg-Witten invariants

Abstract

We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in geometric and arithmetic group theory, that certain hyperbolic 4-manifolds contain L-spaces as hypersurfaces.

8 pages, 2 figures