A secondary Chern-Euler class

Ji-Ping Sha

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arXiv · math/9911269

A secondary Chern-Euler class

Ji-Ping Sha

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Abstract

Let xi be a smooth oriented vector bundle, with n-dimensional fibre, over a smooth manifold M. Denote by xi-hat the fibrewise one-point compactification of xi. The main purpose of this paper is to define geometrically a canonical element Upsilon(xi) in H^n(xi-hat,Q) (H^n(xi-hat,Z) tensor 1/2, to be more precise). The element \Upsilon(\xi) is a secondary characteristic class to the Euler class in the fashion of Chern-Simons.

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Ji-Ping Sha. 1999-11-01. A secondary Chern-Euler class. https://arxiv.org/abs/math/9911269

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