Stiefel-Whitney Classes

  • Jean-Claude HausmannEmail author
Part of the Universitext book series (UTX)


In Sect.  4.7.6, we encountered the Euler class \(e(\xi )\in H^n(B)\) of a vector bundle \(\xi \) of rank \(n\) over \(B\), which sometimes distinguishes between non-isomorphic vector bundles. This is an example of a characteristic class , meaning that it is natural with respect to induced bundles: \(e(f^*\xi )=H^*f(e(\xi ))\) for any continuous map \(f:B'\rightarrow B\). Characteristic classes play a major role in the study of vector bundles.

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University of GenevaGenevaSwitzerland

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