Geometric Constructions of Bundles

  • Glenys Luke
  • Alexander S. Mishchenko
Part of the Mathematics and Its Applications book series (MAIA, volume 447)


To extend the study of the properties of the vector bundles we need further geometric ideas and constructions. This chapter is devoted to the most frequently used constructions which lead to deeper properties of vector bundles. They are Bott periodicity — the main instrument of the calculation of K-theory, linear representations and cohomology operations in K-theory and the Atiyah-Singer formula for calculating of the indices of elliptic operators on compact manifolds. The last of these will be considered in the next chapter.


Tensor Product Vector Bundle Total Space Ring Homomorphism Trivial Bundle 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Glenys Luke
    • 1
  • Alexander S. Mishchenko
    • 2
  1. 1.St. Hugh’s CollegeOxford UniversityOxfordUK
  2. 2.Department of MathematicsMoscow State UniversityMoscowRussia

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