Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

On the Borel transgression in the fibration $G \to G/T$

Pages: 79 – 86

Author

Haibao Duan (Institute of Mathematics, Chinese Academy of Sciences, Beijing, China; amd School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China)

Abstract

Let $G$ be a semisimple Lie group with a maximal torus $T$. We present an explicit formula for the Borel transgression $\tau : H^1 (T) \to H^2 (G/T)$ of the fibration $G \to G/T$. This formula corrects an error in the paper [9], and has been applied to construct the integral cohomology rings of compact Lie groups in the sequel works [4, 6].

Keywords

Lie group, cohomology, Leray-Serre spectral sequence

2010 Mathematics Subject Classification

55T10, 57T10

Full Text (PDF format)

The author’s research is supported by NSFC 11771427, 11661131004.

Received 15 April 2017

Received revised 18 July 2017

Published 3 January 2018