Topological Invariants of Principal G-Bundles with Singularities
- 作者: Arias Amaya F.1, Malakhaltsev M.2
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隶属关系:
- Universidad Tecnológica de Bolívar
- Universidad de los Andes
- 期: 卷 39, 编号 5 (2018)
- 页面: 623-633
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202150
- DOI: https://doi.org/10.1134/S1995080218050013
- ID: 202150
如何引用文章
详细
principal G-bundle with singularities is a principal bundle π: \(\bar P\) → M with structure group \(\bar G\) which reduces to a subgroup G ⊂ \(\bar G\) on the set M \ Σ, where M is an n-dimensional compact manifold and Σ ⊂ M is a k-dimensional submanifold. For example, a vector field on an n-dimensional Riemannian manifold M defines reduction of the orthonormal frame bundle of M to the subgroup O(n − 1) ⊂ O(n) on the set M \ Σ, where Σ is the set of zeros of this vector field. The aim of this paper is to construct topological invariants of principal bundles with singularities. To do this we apply the obstruction theory to the sectionM → \(\bar P\)/Gcorresponding to the reduction and obtain the topological invariant as a class in Hn−k(M,M \ Σ; πn−k−1(\(\bar G\)/G)). We study the properties of this invariants and, in particular, consider cases k = 0 y k = n − 1.
作者简介
F. Arias Amaya
Universidad Tecnológica de Bolívar
编辑信件的主要联系方式.
Email: farias@utb.edu.co
哥伦比亚, Vía a Turbaco Km 1, Cartagena–Bolívar
M. Malakhaltsev
Universidad de los Andes
Email: farias@utb.edu.co
哥伦比亚, Cra. 1 N 18A–12, Bogotá
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