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On the computation of homology of type A real flag manifolds

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arxiv 2306.01127 v3 pith:AHB7GTDG submitted 2023-06-01 math.AT math.CO

Jordan Lambert , Lonardo Rabelo This is my paper · ORCID
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keywords homologyrealflagmanifoldstypeadditionallyassociatedcellular
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In this paper, we present a closed, computable formula for the cellular homology coefficients of real flag manifolds associated with split real forms of type A. We demonstrate the process using movements within the code diagram for permutations. Additionally, we compute the third and fourth homology groups and provide generators for the free part up to the sixth homology group.

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  1. Cellular $\mathbb{A}^1$-Homology from Bruhat Boundary Matrices of Split Semisimple Flag Varieties

    math.AG 2026-07 accept novelty 6.0 of 10

    Cellular A1-homology of split semisimple flag varieties equals reindexed Bruhat boundary matrices times η in Milnor-Witt K-theory, for types A, Bn/Cn/Dn (n≤7), F4, E6, E7.

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