Titlebook: Algebraic Topology from a Homotopical Viewpoint; Marcelo Aguilar,Samuel Gitler,Carlos Prieto Textbook 2002 Springer-Verlag New York 2002 A

有常识

Vector Bundles,In this chapter we shall define and study vector bundles, including their classification. We also examine Grassmann manifolds and universal bundles. Our presentation partly follows Dupont [28].

corn732

Cacophonous

glans-penis

,-Theory,us to those of cohomology as was studied in Chapter 7, but with particularly useful properties, as we shall see in Chapter 10. The foundation for the construction of .-theory is the abelian semigroup Vect(.) of isomorphism classes of vector bundles over . In the course of the chapter we shall give v

Resign

Relations Between Cohomology and Vector Bundles,rmined by the ., which are called the Stiefel-Whitney classes in the case of real vector bundles and are called Chern classes in the complex case. To be more precise, we shall first rely on the fact that ℝℙ. and ℂℙ. are simultaneously Eilenberg-Mac Lane spaces (of type .,1) and K(ℤ,2), respectively)

CROAK

Erythropoietin

离开可分裂

Die Krise der politischen Kommunikation,arious interpretations to .(.), one of these based precisely on the classification results of the previous chapter. Finally, we state the Bott periodicity theorem, whose proof is postponed to Appendix B, and analyze some of its consequences.

STING

drusen

0172-5939 in algebraic geometry as understood by Lawson and Voevodsky. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. The basic concepts of homotopy theory, such as fibrations and cofibrations, are used to construct singular homolo