Convergence and collapsing of CAT$(0)$-lattices

Nicola Cavallucci; Andrea Sambusetti

Convergence and collapsing of CAT$(0)$-lattices

Metric Geometry 2024-05-06 v1 Differential Geometry Group Theory

Authors: Nicola Cavallucci , Andrea Sambusetti

Abstract

We study the theory of convergence for CAT $(0)$ -lattices (that is groups $\Gamma$ acting geometrically on proper, geodesically complete CAT $(0)$ -spaces) and their quotients (CAT $(0)$ -orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how these action can degenerate to a possibly non-discrete limit action. Finally, we prove a compactness theorem for the class of compact CAT $(0)$ -homology orbifolds, and some applications: an isolation result for flat orbispaces and an entropy-pinching theorem.

Keywords

CAT$(0)$-spaces CAT$(0)$-lattices convergence collapsing compactness theorem flat orbispaces entropy-pinching

Cite

@article{arxiv.2405.01595,
  title  = {Convergence and collapsing of CAT$(0)$-lattices},
  author = {Nicola Cavallucci and Andrea Sambusetti},
  journal= {arXiv preprint arXiv:2405.01595},
  year   = {2024}
}

Comments

This is the second half of an old preprint. The first part is about finiteness properties of CAT(0) lattices. This second one concerns limits, possibly with collapsing, of CAT(0)-lattices

Convergence and collapsing of CAT$(0)$-lattices

Abstract

Keywords

Cite

Comments

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