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- W4296787499 abstract "We discuss inequalities between the values of emph{homotopical and cohomological Poincar'e polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic quasi-projective varieties, we prove inequalities between the values of generating functions for the ranks of the graded pieces of the weight and Hodge filtrations of the canonical mixed Hodge structures on homotopy and cohomology groups. Several examples of such mixed Hodge polynomials and related inequalities for rationally elliptic quasi-projective algebraic varieties are presented. One of the consequences is that the homotopical (resp. cohomological) mixed Hodge polynomial of a rationally elliptic toric manifold is a sum (resp. a product) of polynomials of projective spaces. We introduce an invariant called emph{stabilization threshold} $frak{pp} (X;varepsilon)$ for a simply connected rationally elliptic space $X$ and a positive real number $varepsilon$, and we show that the Hilali conjecture implies that $frak{pp} (X;1) le 3$." @default.
- W4296787499 created "2022-09-23" @default.
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- W4296787499 date "2021-07-23" @default.
- W4296787499 modified "2023-10-14" @default.
- W4296787499 title "Ranks of homotopy and cohomology groups for rationally elliptic spaces and algebraic varieties" @default.
- W4296787499 doi "https://doi.org/10.48550/arxiv.2107.11518" @default.
- W4296787499 hasPublicationYear "2021" @default.
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