Bundles and Connections

Kishore Marathe ()
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Kishore Marathe: City University of New York Brooklyn College

Chapter Chapter 4 in Topics in Physical Mathematics, 2010, pp 107-136 from Springer

Abstract: Abstract In 1931 Hopf studied the set [S 3, S 2] of homotopy classes of maps of spheres in his computation of π3(S 2).He showed that π3(S 2) is generated by the class of a certain map that is now well known as the Hopf fibration (see Example 4.5). This fibration decomposes S 3 into subspaces homeomorphic to S 1 and the space of these subsets is precisely the sphere S 2. In 1933 Seifert introduced the term fiber space to describe this general situation. The product of two topological spaces is trivially a fiber space, but the example of the Hopf fibration shows that a fiber space need not be a global topological product. It continues to be a local product and is now referred to as a fiber bundle.

Keywords: Vector Bundle; Fiber Bundle; Principal Bundle; Linear Connection; Grassmann Manifold (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-84882-939-8_4

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