Journal of Mathematics of Kyoto University

An upper bound for the 3-primary homotopy exponent of the exceptional Lie group $E_7$

Stephen D. Theriault

Abstract

A new homotopy fibration is constructed at the prime 3 which shows that the quotient group $E_{7}/F_{4}$ is spherically resolved. This is then used to show that the 3-primary homotopy exponent of $E_{7}$ is bounded above by $3^{23}$, which is at most four powers of 3 from being optimal.

Article information

Source
J. Math. Kyoto Univ., Volume 47, Number 3 (2007), 541-564.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281023

Digital Object Identifier
doi:10.1215/kjm/1250281023

Mathematical Reviews number (MathSciNet)
MR2402514

Zentralblatt MATH identifier
1163.55010

Subjects
Primary: 55Q52: Homotopy groups of special spaces

Citation

Theriault, Stephen D. An upper bound for the 3-primary homotopy exponent of the exceptional Lie group $E_7$. J. Math. Kyoto Univ. 47 (2007), no. 3, 541--564. doi:10.1215/kjm/1250281023. https://projecteuclid.org/euclid.kjm/1250281023