有理同伦中向量束的Thom空间的权分解

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2019-07-12 DOI:10.1007/s40062-019-00243-2

Urtzi Buijs, Federico Cantero Morán, Joana Cirici

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引用次数: 3

摘要

在子流形可表示类理论的启发下，研究了向量束的同伦空间的有理同伦理论。我们首先在有理同伦水平上给出了一个Thom同构，通过去掉基的幂零性和束的可定向性的假设，扩展了f - oprea - tanr的工作。然后，利用有理同伦的权分解理论，给出了类的子流形可表示性的判据，推广了Papadima的结果。在此过程中，我们研究了形式问题，并给出了Thom空间的Massey积的公式。最后，我们将权重分解理论与混合Hodge理论联系起来，并将我们的结果应用于动机Thom空间。

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Weight decompositions of Thom spaces of vector bundles in rational homotopy

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.

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.