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

@article{Baues2018IsometryGW, title={Isometry groups with radical, and aspherical Riemannian manifolds with large symmetry I}, author={O. Baues and Y. Kamishima}, journal={arXiv: Differential Geometry}, year={2018} }

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 symmetry if it admits an infrasolv tower whose base is a locally homogeneous space. We…

## One Citation

Locally homogeneous aspherical Sasaki manifolds

- Mathematics
- 2019

Let $G/H$ be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold $\Gamma\big\backslash G/H$ is by definition a quotient of $G/H$ by a discrete uniform…

## References

SHOWING 1-10 OF 29 REFERENCES

Compact Clifford-Klein forms of symmetric spaces

- Mathematics
- 1963

We recall that a Riemannian manifold X is symmetric, in the sense of Cartan, if it is connected and if every point x E X is an isolated fixed point of an involutive isometry s, of X. The map s, is…

The Group of Isometries of a Riemannian Manifold

- Mathematics
- 1939

In the classical theory of groups of motions (isometries) of a Riemannian space,1 neither "whole" groups nor "whole" spaces were ever considered, but only "group germs" and spaces in the neighborhood…

Isometries, rigidity and universal covers

- Mathematics
- 2005

The goal of this paper is to describe all closed, aspherical Riemannian manifolds M whose universal covers M have have a nontrivial amount of symmetry. By this we mean that Isom(M) is not discrete.…

Infra-solvmanifolds and rigidity of subgroups in solvable linear algebraic groups

- Mathematics
- 2004

Abstract We give a new proof that compact infra-solvmanifolds with isomorphic fundamental groups are smoothly diffeomorphic. More generally, we prove rigidity results for manifolds which are…

On the first Betti number of a constant negatively curved manifold

- Mathematics
- 1976

constant negatively curved n-dimensional manifolds with arbitrarily large first Betti number. In fact we show that any constant negatively curved manifold whose fundamental group is an arithmetic…

On fundamental groups of complete affinely flat manifolds

- Mathematics
- 1977

First some definitions. A group I is virtually polycyclic if it has a subgroup r, of finite index which is polycyclic, that is, admits a finite composition series r, 3 r, 3 -1.3 r, = (1) so that each…

Differential Geometry, Lie Groups, and Symmetric Spaces

- Mathematics
- 1978

Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric…

Surgery on compact manifolds

- Mathematics
- 1970

Preliminaries: Note on conventions Basic homotopy notions Surgery below the middle dimension Appendix: Applications Simple Poincare complexes The main theorem: Statement of results An important…

On the Existence of Slices for Actions of Non-Compact Lie Groups

- Mathematics
- 1961

If G is a topological group then by a G-space we mean a completely regular space X together with a fixed action of G on X. If one restricts consideration to compact Lie groups then a substantial…

Discrete subgroups of Lie groups

- Mathematics
- 1972

Preliminaries.- I. Generalities on Lattices.- II. Lattices in Nilpotent Lie Groups.- III. Lattices in Solvable Lie Groups.- IV. Polycyclic Groups and Arithmeticity of Lattices in Solvable Lie…