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Equivariant maps of joins of finite G-sets and an application to critical point theory

Danuta Rozpłoch-Nowakowska (1992)

Annales Polonici Mathematici

A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function f : S n , where G is a finite nontrivial group acting freely and orthogonally on n + 1 0 . Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk’s Antipodal Theorem for equivariant maps of joins of G-sets.

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M M ( ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ) for locally symmetric spaces. Moreover, M ( ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

On G -sets and isospectrality

Ori Parzanchevski (2013)

Annales de l’institut Fourier

We study finite G -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If M is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then M has isospectral non-isometric covers.

On rank one symmetric space

Inkang Kim (2004/2005)

Séminaire de théorie spectrale et géométrie

In this paper we survey some recent results on rank one symmetric space.

On symmetrically growing bodies.

Reuven Segev (1997)

Extracta Mathematicae

This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.

Representation of a gauge group as motions of a Hilbert space

Clara Lucía Aldana Domínguez (2004)

Annales mathématiques Blaise Pascal

This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second...

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