Abstract
We come back to involutions to make some observations that did not fit into the framework of Chapter IV. Given a fixed point free involution (T, B) and an n-plane bundle r:E → B/T, we define another n-plane bundle ř: Ě → B/T, which we call the twist of r by (T, B). In the manner of Borel-Hirzebruch, we compute its Whitney class. In section 32, we make one application showing some of the influence of the homology of the total space on the Whitney classes of normal bundles to the fixed point set. In section 33, we give some generalizations of the famed Borsuk antipode theorems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1964 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Conner, P.E., Floyd, E.E. (1964). Differentiable involutions and bundles. In: Differentiable Periodic Maps. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-41633-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-662-41633-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-41635-8
Online ISBN: 978-3-662-41633-4
eBook Packages: Springer Book Archive