Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

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

Pages: 79 – 86

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n1.a6

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

Received 15 April 2017

Received revised 18 July 2017

Published 3 January 2018