Hopf Fibrations and Hurwitz-Radon Numbers
Hopf Fibrations and Hurwitz-Radon Numbers
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Hopf 纤维和 Hurwitz-Radon 数
DOI：
10.1007/s00283-015-9618-x
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Tabachnikov
中科院分区：
文献类型：
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作者：
V. Ovsienko;S. Tabachnikov
提交的作品应上传到http://tmin.edmgr.com或直接发送到谢尔盖Tabachnikov，tabachni@math.psu.edu H opf纤维化是一个美丽的拓扑结构，代表了一个三维球体作为一个不相交的工会成对链接的大圆。从它在YouTube上的存在来看，它几乎是大众文化的对象;见[23]的采样器。对于可视化，我们也强烈推荐电影“维度”[3]。霍普夫纤维化是由著名的德国几何学家和拓扑学家海因茨·霍普夫在1931年定义和研究的[16]。从某种意义上说，当代代数拓扑学是随着霍普夫纤维化而发展起来的：特征类理论、同伦理论和K-理论的发展受到了霍普夫纤维化研究的很大影响;见[4，5，8，13，14]。霍普夫纤维化出现在数学和物理的其他领域，包括流体动力学，规范理论，宇宙学和基本粒子[22]。事实上，存在四个纤维丛，称为霍普夫纤维化，其纤维、全空间和基底都是球面：
Submissions should be uploaded to http://tmin.edmgr.com or sent directly to Sergei Tabachnikov, tabachni@math.psu.edu H opf fibration is a beautiful topological construction representing a 3-dimensional sphere as a disjoint union of pairwise linked great circles. Judging by its presence on YouTube, it is almost an object of mass culture; see [23] for a sampler. For visualization, we also strongly recommend the film ‘‘Dimensions’’ [3]. Hopf fibration was defined and studied by the famous German geometer and topologist Heintz Hopf in 1931 [16]. In a sense, contemporary algebraic topology has grown up with the Hopf fibration: the development of the theory of characteristic classes, homotopy theory, and K-theory was much influenced by the study of Hopf fibration; see [4, 5, 8, 13, 14]. Hopf fibration appears in other areas of mathematics and physics, including fluid dynamics, gauge theories, cosmology, and elementary particles [22]. In fact, there exist four fiber bundles, called the Hopf fibrations, whose fibers, total spaces, and bases are spheres: