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Odd primary homotopy types of the gauge groups of exceptional Lie groups


Authors: Sho Hasui, Daisuke Kishimoto, Tseleung So and Stephen Theriault
Journal: Proc. Amer. Math. Soc. 147 (2019), 1751-1762
MSC (2010): Primary 55P15; Secondary 54C35
DOI: https://doi.org/10.1090/proc/14333
Published electronically: January 8, 2019
MathSciNet review: 3910439
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Abstract: The $p$-local homotopy types of gauge groups of principal $G$-bundles over $S^4$ are classified when $G$ is a compact connected exceptional Lie group without $p$-torsion in homology except for $(G,p)=(\mathrm {E}_7,5)$.


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Additional Information

Sho Hasui
Affiliation: Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan
MR Author ID: 1085016
Email: s.hasui@math.tsukuba.ac.jp

Daisuke Kishimoto
Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan
MR Author ID: 681652
ORCID: 0000-0002-7837-8818
Email: kishi@math.kyoto-u.ac.jp

Tseleung So
Affiliation: Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
MR Author ID: 1266815
Email: tls1g14@soton.ac.uk

Stephen Theriault
Affiliation: Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
MR Author ID: 652604
Email: s.d.theriault@soton.ac.uk

Keywords: Gauge group, homotopy-type, exceptional Lie group, Samelson product
Received by editor(s): March 27, 2018
Received by editor(s) in revised form: June 12, 2018
Published electronically: January 8, 2019
Additional Notes: The second author’s work was supported by JSPS KAKENHI Grant Number 17K05248.
Communicated by: Mark Behrens
Article copyright: © Copyright 2019 American Mathematical Society