Manifolds without real projective or flat conformal structures

TL;DR

This paper constructs high-dimensional closed manifolds that lack real projective and flat conformal structures, yet have non-elementary Gromov hyperbolic fundamental groups, using relative strict hyperbolization techniques.

Contribution

It provides explicit examples of manifolds without certain geometric structures, expanding understanding of the relationship between topology and geometric structures in high dimensions.

Findings

Existence of manifolds without real projective structures

Existence of manifolds without flat conformal structures

Fundamental groups are non-elementary Gromov hyperbolic

Abstract

In any dimension at least five we construct examples of closed smooth manifolds with the following properties: 1) they have neither real projective nor flat conformal structures; 2) their fundamental group is a non-elementary Gromov hyperbolic group. These examples are obtained via relative strict hyperbolization.