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Splitting of gauge groups


Authors: Daisuke Kishimoto and Akira Kono
Journal: Trans. Amer. Math. Soc. 362 (2010), 6715-6731
MSC (2000): Primary 57S05, 55R70; Secondary 54C35
DOI: https://doi.org/10.1090/S0002-9947-2010-05207-9
Published electronically: August 3, 2010
MathSciNet review: 2678992
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Abstract: Let $ G$ be a topological group and let $ P$ be a principal $ G$-bundle over a based space $ B$. We denote the gauge group of $ P$ by $ \mathcal{G}(P)$ and the based gauge group of $ P$ by $ \mathcal{G}_0(P)$. Then the inclusion of the basepoint of $ B$ induces the exact sequence of topological groups $ 1\to\mathcal{G}_0(P)\to\mathcal{G}(P)\to G\to 1$. We study the splitting of this exact sequence in the category of $ A_n$-spaces and $ A_n$-maps in connection with the triviality of the adjoint bundle of $ P$ and with the higher homotopy commutativity of $ G$.


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Additional Information

Daisuke Kishimoto
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: kishi@math.kyoto-u.ac.jp

Akira Kono
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Email: kono@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-2010-05207-9
Keywords: Gauge group, fibrewise $A_{n}$-map, evaluation fibration, higher homotopy commutativity
Received by editor(s): June 16, 2009
Received by editor(s) in revised form: September 18, 2009
Published electronically: August 3, 2010
Additional Notes: The second author was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B)
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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