Cellularization for exceptional spherical space forms and the flag manifold of $SL_3(\mathbb{R})$

Rocco Chirivi; Arthur Garnier; Mauro Spreafico

doi:10.1016/j.exmath.2022.02.001

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arXiv · 2006.14417

Cellularization for exceptional spherical space forms and the flag manifold of $SL_3(\mathbb{R})$

Rocco Chirivi·Arthur Garnier·Mauro Spreafico

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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 $SL_3(\mathbb{R})$.

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Rocco Chirivi, Arthur Garnier, Mauro Spreafico. 2020-06-25. Cellularization for exceptional spherical space forms and the flag manifold of $SL_3(\mathbb{R})$. https://doi.org/10.1016/j.exmath.2022.02.001

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