Characteristic classes as complete obstructions

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2019-03-13 DOI:10.1007/s40062-019-00232-5

Martina Rovelli

引用次数: 0

Abstract

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a single fiber of the bundle. Afterwards, we define a family of invariants of principal bundles that detect the number of group reductions that a principal bundle admits. We prove that they fit into a long exact sequence of abelian groups, together with the cohomology of the base space and the cohomology of the classifying space of the structure group.

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作为完全障碍物的特征类

在本文的第一部分中，我们给出了特征类作为结构群约化和仅在束的单个纤维上先验定义的某同态的等变扩展存在性障碍的统一解释。然后，我们定义了一类检测主束允许的群约简数的主束不变量。证明了它们与基空间的上同调和结构群的分类空间的上同调合为一长精确的阿贝尔群序列。

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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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.