## Journal of Mathematics of Kyoto University

### The 5-primary homotopy exponent of the exceptional Lie group $E_8$

Stephen D. Theriault

#### Abstract

We construct a new homotopy fibration at the prime 5, involving $E_{8}$ and Harper’s rank two finite mod-5 $H$-space. We then use this to show that the 5-primary homotopy exponent of $E_{8}$ is bounded above by $5^{31}$, which is at most one power of 5 from being optimal.

#### Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 3 (2004), 569-593.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250283084

Digital Object Identifier
doi:10.1215/kjm/1250283084

Mathematical Reviews number (MathSciNet)
MR2103783

Zentralblatt MATH identifier
1088.55011

Subjects
Primary: 55Q52: Homotopy groups of special spaces

#### Citation

Theriault, Stephen D. The 5-primary homotopy exponent of the exceptional Lie group $E_8$. J. Math. Kyoto Univ. 44 (2004), no. 3, 569--593. doi:10.1215/kjm/1250283084. https://projecteuclid.org/euclid.kjm/1250283084