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Fibre bundles

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  • "Fibre bundles"
  • "纤维丛"
  • "Qian wei cong"
  • "Xian wei cong"@en

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  • "Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles."
  • "The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950 the defini tion of fibre bundle had been clearly formulated, the homotopy classifica tion of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians, Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gave a coherent treatment of the subject up to that time. About 1955 Milnor gave a construction of a universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal. During the five years from 1950 to 1955, Hirzebruch clarified the notion of characteristic class and used it to prove a general Riemann-Roch theorem for algebraic varieties. This was published in his Ergebnisse Monograph. A systematic development of characteristic classes and their applications to manifolds is given in Part III and is based on the approach of Hirze bruch as modified by Grothendieck."

genre

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  • "Electronic books"@en
  • "Electronic books"
  • "Einführung"

name

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  • "Fibre bundles 2e ed"
  • "Fibre bundles (third edition)"
  • "Rassloennye prostranstva"
  • "Fibre Bundles"
  • "Fibre Bundles"@it
  • "Fibre bundles"@en
  • "Fibre bundles"
  • "Fibre bundles : (by) dale husemoller. 2nd ed"
  • "Расслоенные пространства = Fibre bundles"
  • "Rassloennye prostranstva = Fibre bundles"
  • "Fiber bundles"

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