Abstract
The stable homotopy and cohomotopy groups. Spectra. Vector bundles, Thom spaces and Thom spectra. Bordism and the Pontryagin–Thom isomorphism. S-duality. The Atiyah S-duality for a manifold. The Wall S-duality for a geometric Poincaré complex. The stable cohomotopy Thom and Euler classes.
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Crabb, M., Ranicki, A. (2017). Stable Homotopy Theory. In: The Geometric Hopf Invariant and Surgery Theory. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-71306-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-71306-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71305-2
Online ISBN: 978-3-319-71306-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)