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Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry, I

Oliver Baues and Yoshinobu Kamishima

Geometry & Topology 27 (2023) 1–50
Abstract

Every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infrasolv fibers, which is called its infrasolv tower. The tower arises from the solvable radicals of isometry group actions on the universal covers. Its length and the geometry of its base measure the degree of continuous symmetry of an aspherical Riemannian manifold. We say that the manifold has large local symmetry if it admits a tower of orbibundle fibrations with locally homogeneous fibers whose base is a locally homogeneous space. We construct examples of aspherical manifolds with large local symmetry which do not support any locally homogeneous Riemannian metrics.

Keywords
aspherical manifolds, divisible manifolds, infrasolv tower, solvable radical, large symmetry, proper group actions, infrasolv manifolds, locally homogeneous manifolds, smooth toral actions
Mathematical Subject Classification 2010
Primary: 53C12, 53C30, 57S30
References
Publication
Received: 3 April 2019
Revised: 7 October 2020
Accepted: 2 October 2021
Published: 1 May 2023
Proposed: Martin R Bridson
Seconded: Paul Seidel, Anna Wienhard
Authors
Oliver Baues
Department of Mathematics
University of Fribourg
Fribourg
Switzerland
Yoshinobu Kamishima
Department of Mathematics
Josai University
Sakado
Japan

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