An Index of an Equivariant Vector Field and Addition Theorems for Pontrjagin Characteristic Classes

Details An Index of an Equivariant Vector Field and Addition Theorems for Pontrjagin Characteristic Classes An Index of an Equivariant Vector Field and Addition Theorems for Pontrjagin Characteristic Classes

2000-02-21

arxiv.org/abs/math/0002172v1

Mathematics

Algebraic Topology

Scientific paper

The theory of indices of Morse--Bott vector fields on a manifold is constructed and the famous localization problem for the transfer map is solved on its base in the present paper. As a consequence, we obtained addition theorems for the universal Pontrjagin characteristic classes in cobordisms. These results gave us a possibility to complete the construction, which was begun more than twenty years ago, of the universal characteristic classes' theory.

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