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K-Theory pp 270-300 | Cite as

Some Applications of K-Theory

  • Max Karoubi
Part of the Classics in Mathematics book series (CLASSICS)

Abstract

Let α: S n - 1 S n - 1 be a continuous map. Then \(\tilde K_\mathbb{C}^{n - 1}\left( {{S^{n - 1}}} \right) \approx \mathbb{Z}\), and α induces an endomorphism of of the form xλx where λ. The integer λ is called the degree of α, and is denoted by deg(α). In particular, if α is a homeomorphism, we have deg(α) = ± 1. It is possible to prove (cf. Hu [1]) that π n - 1(S n - 1) ≈ , where the isomorphism is given by the degree. However, we do not require this result in this section.

Keywords

Vector Bundle Line Bundle Euler Class Sphere Bundle Complex Vector Bundle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Max Karoubi
    • 1
  1. 1.U.E.R. de Mathématiques, Tour 45-55Université Paris VIIParis Cedex 05France

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