Geometric Constructions of Bundles
- 438 Downloads
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.