Rational ellipticity of $G$-manifolds from their quotients

Elahe Khalili Samani; Marco Radeschi

Rational ellipticity of $G$-manifolds from their quotients

Differential Geometry 2024-12-24 v2

Authors: Elahe Khalili Samani , Marco Radeschi

Abstract

We prove that if a compact, simply connected Riemannian $G$ -manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes most conditions on rational ellipticity, is a particular case of a more general result involving manifold submetries.

Keywords

rational ellipticity G-manifold orbit space topological entropy manifold submetry quotient space

Cite

@article{arxiv.2312.08202,
  title  = {Rational ellipticity of $G$-manifolds from their quotients},
  author = {Elahe Khalili Samani and Marco Radeschi},
  journal= {arXiv preprint arXiv:2312.08202},
  year   = {2024}
}

Comments

New exposition and corrections after report. Version to appear in Compos. Math

Rational ellipticity of $G$-manifolds from their quotients

Abstract

Keywords

Cite

Comments

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