Cellularization for exceptional spherical space forms and the flag manifold of $S{L}_3(\mathbb{R})$

Abstract

We construct an explicit equivariant cellular decomposition of the $(4n-1)$-sphere with respect to binary polyhedral groups, and describe the associated cellular homology chain complex. As a corollary of the binary octahedral case, we deduce an ${\mathfrak{S}}_3$-equivariant decomposition of the flag manifold of $S{L}_3(\mathbb{R})$.

submitted to Transformation Groups

References in corpus (1)

• Remarks on the cohomology of finite fundamental groups of 3-manifolds

Cited by in corpus (2)

• Equivariant triangulations of tori of compact Lie groups and hyperbolic extension to non-crystallographic Coxeter groups
• Dirichlet-Voronoi domain and injectivity radius of flag manifolds -- equivariant cell structure on $O(3)/O(1{)}^3$