论文标题
dirichlet-voronoi域和标志歧管的注射率半径 - $ O（3）/o（1）^3 $上的epivariant细胞结构
Dirichlet-Voronoi domain and injectivity radius of flag manifolds -- equivariant cell structure on $O(3)/O(1)^3$
论文作者
论文摘要
在这项工作的第一部分中，我们研究了Dirichlet-Voronoi结构域，用于riemannian歧管的离散等轴测组，鉴于在同质（完整的，真实的）标志歧管上构建细胞结构，相对于WEYL组的作用而言。我们给出了一般的结果，可以从域上的可允许的结构中构建这样的结构。特别是，注射性半径在该方法中起关键作用。第二部分始于（真实和复杂）标志歧管的注入性半径的计算；在第一部分中开发的方法的应用的第一步。然后，在四元组代数的帮助下，我们研究了标志歧管$ o（3）/o（3）/o（1）^3 $ $ sl_3（\ Mathbb {r}）$：我们证明，第一部分的结果适用并导致了新的$ \ mathfrak {s} _3 $ - equiant Complate unt的Complact un It，它的Complact n it it it it It It It n it it unt $ \ mathbb {z} [\ mathfrak {s} _3] $ - 模块。
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 (complete, real) flag manifolds, equivariant with respect to the action of the Weyl group. We give general results, allowing to build such a structure from an admissible one on the domain. In particular, the injectivity radius plays a key role in the method. The second part starts with the computation of the injectivity radius of (real and complex) flag manifolds; a first step towards the application of the method developed in the first part. Then, with the help of the quaternion algebra, we investigate the particular case of the flag manifold $O(3)/O(1)^3$ of $SL_3(\mathbb{R})$: we prove that the results of the first part apply and derive a new $\mathfrak{S}_3$-equivariant cell structure on it, whose cellular complex of $\mathbb{Z}[\mathfrak{S}_3]$-modules is determined.
