Arthur Garnier

activity

20242026

collaborators

3 papers

math.DG2026

Dirichlet-Voronoi domain and injectivity radius of flag manifolds -- equivariant cell structure on $O (3) / O (1)^{3}$

Arthur Garnier

In the first part of this work, we study Dirichlet--Voronoi domains for discrete isometry groups of Riemannian manifolds, in view of constructing cell structures on homogeneous (co…

math.CO2025

Fundamental polytope for the isometry group of an alcove

Lucas Seco, Arthur Garnier, Karl-Hermann Neeb

A fundamental alcove $A$ is a tile in a paving of a vector space $V$ by an affine reflection group $W_{aff}$ . Its geometry encodes essential features of $W_{\mat…

math.AT2024

Fundamental polytope for the Weyl group acting on a maximal torus of a compact Lie group

Arthur Garnier

We provide a fundamental domain for the action of the finite Weyl group on a maximal torus of a compact Lie group of the corresponding type. The general situation is reduced to the…

Dirichlet-Voronoi domain and injectivity radius of flag manifolds -- equivariant cell structure on O(3)/O(1)3

Fundamental polytope for the isometry group of an alcove

Fundamental polytope for the Weyl group acting on a maximal torus of a compact Lie group

Dirichlet-Voronoi domain and injectivity radius of flag manifolds -- equivariant cell structure on $O (3) / O (1)^{3}$