低维流形的 W 三维性

Pub Date : 2024-06-03 DOI:10.1007/s00229-024-01575-x

Aritra C. Bhattacharya, Bikramjit Kundu, Aniruddha C. Naolekar

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引用次数: 0

摘要

如果 X 上的每个实向量束 \(\alpha \)的总 Stiefel-Whitney 类 \(w(\alpha)\)都是 1，那么空间 X 就是 W-琐碎的。由 Milnor 的一个结果可知，如果 X 是维数为 1、2、4 或 8 的可定向封闭光滑流形，那么 X 就不是 W-琐碎的。在本注释中，我们完全描述了维 3、维 5 和维 6 的 W 三维可定向连通封闭光滑流形的特征。在维数 7 中，我们描述了可定向连通闭合光滑 7manifold 是 W-trivial 的必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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W-triviality of low dimensional manifolds

A space X is W-trivial if for every real vector bundle \(\alpha \) over X the total Stiefel-Whitney class \(w(\alpha )\) is 1. It follows from a result of Milnor that if X is an orientable closed smooth manifold of dimension 1, 2, 4 or 8, then X is not W-trivial. In this note we completely characterize W-trivial orientable connected closed smooth manifolds in dimensions 3, 5 and 6. In dimension 7, we describe necessary conditions for an orientable connected closed smooth 7-manifold to be W-trivial.

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