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http://hdl.handle.net/2445/192219
Title: | Weight decompositions of Thom spaces of vector bundles in rational homotopy |
Author: | Buijs, Urtzi Cantero Morán, Federico Cirici, Joana |
Keywords: | Teoria de l'homotopia Topologia diferencial Homotopy theory Differential topology |
Issue Date: | 12-Jul-2019 |
Publisher: | Springer Nature |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s40062-019-00243-2 |
It is part of: | Journal of Homotopy and Related Structures, 2019, vol. 15, p. 1-26 |
URI: | http://hdl.handle.net/2445/192219 |
Related resource: | https://doi.org/10.1007/s40062-019-00243-2 |
ISSN: | 2193-8407 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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