Using the Grothendieck construction in the preceding chapter, we defined the functors KG for real and complex G-bundles and the Atiyah real KR G by mapping the semiring of G-vector bundles into its ring envelope. We saw that the basic properties of the equivariant versions of vector bundle theory have close parallels with the usual vector bundle theory, and the same is true for the related relative K-theories. This we carry further in this chapter for the version of topological K-theory that has close relations to index theory.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Atiyah, M.F., Segal, G.B.: Equivariant K-theory and completion J.Differential Geom. 3: 1–18 (1969)
Atiyah, M.F., Segal, G.B.: The index of elliptic operators II. Ann. of Math. (2) Annals of Mathematics, Second Series 87: 531–545 (1968)
Segal, G.B.: Equivariant K-theory. Publ Math.I.H.E.S. Paris 34: 129–151 (1968)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Husemöller, D., Joachim, M., Jurčo, B., Schottenloher, M. (2008). Equivariant K-Theory Functor KG : Periodicity, Thom Isomorphism, Localization, and Completion. In: Basic Bundle Theory and K-Cohomology Invariants. Lecture Notes in Physics, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74956-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-74956-1_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74955-4
Online ISBN: 978-3-540-74956-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)