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Rational ellipticity of G-manifolds from their quotients

Part of: Variational problems in infinite-dimensional spaces Global differential geometry

Published online by Cambridge University Press:  09 June 2025

Elahe Khalili Samani Open the ORCID record for Elahe Khalili Samani [Opens in a new window]  and
Marco Radeschi Open the ORCID record for Marco Radeschi [Opens in a new window]
Elahe Khalili Samani
Affiliation:
Department of Mathematics, Clark University, Worcester, MA 01610, USA ekhalilisamani@clarku.edu
Marco Radeschi
Affiliation:
Università degli Studi di Torino,Dipartimento di matematica “G. Peano”, Via Carlo Alberto 10, 10123 Torino (TO), Italy marco.radeschi@unito.it
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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

rationally ellipticsubmetryisometric group actiontopological entropy

MSC classification

Primary: 53C22: Geodesics 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 2 , June 2025 , pp. 244 - 256
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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