We construct an explicit equivariant cellular decomposition of the (4n−1)-sphere with respect to binary polyhedral groups, and describe the associated cellular chain complex. As a corollary of the binary octahedral case, we deduce an S3-equivariant decomposition of the flag manifold of SL3(R).
Chirivì, R., Garnier, A., Spreafico, M. (2022). Cellularization for exceptional spherical space forms and the flag manifold of SL3(R). EXPOSITIONES MATHEMATICAE, 40(3), 572-604 [10.1016/j.exmath.2022.02.001].
Cellularization for exceptional spherical space forms and the flag manifold of SL3(R)
Spreafico, M
2022
Abstract
We construct an explicit equivariant cellular decomposition of the (4n−1)-sphere with respect to binary polyhedral groups, and describe the associated cellular chain complex. As a corollary of the binary octahedral case, we deduce an S3-equivariant decomposition of the flag manifold of SL3(R).
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