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A note on characteristic classes

Jianwei Zhou (2006)

Czechoslovak Mathematical Journal

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

Correction for the paper “ S 3 -bundles and exotic actions”

T. E. Barros (2001)

Bulletin de la Société Mathématique de France

In [R] explicit representatives for S 3 -principal bundles over S 7 are constructed, based on these constructions explicit free S 3 -actions on the total spaces are described, with quotients exotic 7 -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic 7 -spheres that occur as quotients of the free S 3 -actions described above.

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