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Accepted version

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2019-07-12

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/192219

Weight decompositions of Thom spaces of vector bundles in rational homotopy

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https://doi.org/10.1007/s40062-019-00243-2

Abstract

Motivated by the theory of representability classes by submanifolds, we study the rational homotopy theory of Thom spaces of vector bundles. We first give a Thom isomorphism at the level of rational homotopy, extending work of Félix-Oprea-Tanré by removing hypothesis of nilpotency of the base and orientability of the bundle. Then, we use the theory of weight decompositions in rational homotopy to give a criterion of representability of classes by submanifolds, generalising results of Papadima. Along the way, we study issues of formality and give formulas for Massey products of Thom spaces. Lastly, we link the theory of weight decompositions with mixed Hodge theory and apply our results to motivic Thom spaces.

Subject

Teoria de l'homotopia, Topologia diferencial

Subject (English)

Homotopy theory, Differential topology

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BUIJS, Urtzi, CANTERO MORÁN, Federico and CIRICI, Joana. Weight decompositions of Thom spaces of vector bundles in rational homotopy. Journal of Homotopy and Related Structures. 2019. Vol. 15, num. 1-26. ISSN 2193-8407. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/192219

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