Hyperbolic four-manifolds with vanishing Seiberg-Witten invariants

TL;DR

This paper proves the existence of hyperbolic four-manifolds with zero Seiberg-Witten invariants by linking geometric group theory results to the presence of L-spaces as hypersurfaces within these manifolds.

Contribution

It demonstrates the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, confirming a conjecture of Claude LeBrun through geometric and arithmetic group theory methods.

Findings

Hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants exist.

Certain hyperbolic 4-manifolds contain L-spaces as hypersurfaces.

The results connect geometric group theory with 4-manifold 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.