A compactness theorem for locally homogeneous spaces

Francesco Pediconi

A compactness theorem for locally homogeneous spaces

Differential Geometry 2021-01-19 v2

Authors: Francesco Pediconi

Abstract

We prove the existence and uniqueness of geometric models of local isometry classes of locally homogeneous spaces with sectional curvature $|\operatorname{sec}|\leq 1$ . Moreover, we show that the set of geometric models is compact in the pointed $\mathcal{C}^{1,\alpha}$ -topology.

Keywords

general topology algebraic topology topological groups

Cite

@article{arxiv.1911.05062,
  title  = {A compactness theorem for locally homogeneous spaces},
  author = {Francesco Pediconi},
  journal= {arXiv preprint arXiv:1911.05062},
  year   = {2021}
}

Comments

14 pages. Some minor modifications. Accepted for publication in Ann. Sc. Norm. Super. Pisa Cl. Sci

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