Abstract
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.
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© 1998 Springer Science+Business Media Dordrecht
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Luke, G., Mishchenko, A.S. (1998). Geometric Constructions of Bundles. In: Vector Bundles and Their Applications. Mathematics and Its Applications, vol 447. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6923-4_3
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DOI: https://doi.org/10.1007/978-1-4757-6923-4_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4802-1
Online ISBN: 978-1-4757-6923-4
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