• arithmetic manifolds
• four-manifolds
• hyperbolic geometry
• Seiberg-Witten invariants

The aim of the thesis is to show the existence of hyperbolic four-manifolds whose Seiberg-Witten invariants vanish, following the homonymous article by I. Agol and F. Lin.
This is done by using a vanishing result for four-manifolds admitting a separating L-space, and by exhibiting a L-space that embeds in separating way into a hyperbolic four-manifold. To do this, we use some recent results about the embeddings of arithmetic manifolds of simplest type due to S. Kolpakov, A. Reid and L. Slavich.