A small closed convex projective 4-manifold via Dehn filling

TL;DR

This paper constructs a new example of a closed convex projective four-manifold with small positive Euler characteristic by applying Dehn filling to a cusped hyperbolic four-manifold through a continuous deformation.

Contribution

It provides the first explicit convex projective Dehn filling construction for a four-manifold, expanding the known examples in higher-dimensional convex projective geometry.

Findings

Successfully constructed a closed convex projective 4-manifold.

Demonstrated a continuous path of projective cone-manifolds leading to the filling.

Achieved a manifold with small positive Euler characteristic.

Abstract

In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a cusped hyperbolic four-manifold through a continuous path of projective cone-manifolds.