The Space of Strictly-convex Real-projective structures on a closed manifold

Daryl Cooper; Stephan Tillmann

The Space of Strictly-convex Real-projective structures on a closed manifold

Geometric Topology 2025-12-02 v3

Authors: Daryl Cooper , Stephan Tillmann

Abstract

This is an expository proof that, if $M$ is a compact $n$ -manifold with no boundary, then the set of holonomies of strictly-convex real-projective structures on $M$ is a subset of $\operatorname{Hom}(\pi_1M,\operatorname{PGL}(n+1,\mathbb R))$ that is both open and closed.

Keywords

strictly-convex real-projective structures closed manifold holonomy pgl open and closed subset

Cite

@article{arxiv.2009.06582,
  title  = {The Space of Strictly-convex Real-projective structures on a closed manifold},
  author = {Daryl Cooper and Stephan Tillmann},
  journal= {arXiv preprint arXiv:2009.06582},
  year   = {2025}
}

Comments

Publication version. Improved exposition and figures

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