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Pré-Publication, Document De Travail Année : 2020

CELLULARIZATION FOR EXCEPTIONAL SPHERICAL SPACE FORMS AND APPLICATION TO FLAG MANIFOLDS

Résumé

Given a finite group acting freely and isometrically on a Euclidean sphere, it is natural to look for an equivariant cellular decomposition of the sphere. In this way, one obtains a cellular decomposition of the quotient manifold, called a spherical space form. In this paper, we apply the method developed by the first and thirs authors, using the so-called orbit polytope, to construct an explicit equivariant cellular decomposition of the (4n − 1)-sphere with respect to the binary octahedral and the binary icosahedral groups, and describe the associated cellular homology chain complex. As an application, we find free resolutions of the constant module over these groups and deduce their integral cohomology. Moreover, we use the octahedral case to describe a cellular structure on the flag manifold of R 3 that is equivariant with respect to the Weyl group action.
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Dates et versions

hal-02945044 , version 1 (22-09-2020)
hal-02945044 , version 2 (01-05-2021)
hal-02945044 , version 3 (27-08-2022)

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  • HAL Id : hal-02945044 , version 1

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Rocco Chirivì, Arthur Garnier, Mauro Spreafico. CELLULARIZATION FOR EXCEPTIONAL SPHERICAL SPACE FORMS AND APPLICATION TO FLAG MANIFOLDS. 2020. ⟨hal-02945044v1⟩
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