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Conjugate $SU(r)$-connections and holonomy groups


Author: Jin-Hong Kim
Journal: Proc. Amer. Math. Soc. 128 (2000), 865-871
MSC (2000): Primary 53C05
DOI: https://doi.org/10.1090/S0002-9939-99-05457-X
Published electronically: September 9, 1999
MathSciNet review: 1690994
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Abstract: In this article we show that when the structure group of the reducible principal bundle $P$ is $SU(r)$ and $Q\subset P$ is an $SO(r)$-subbundle of $P$, the rank of the holonomy group of a connection which is gauge equivalent to its conjugate connection is less than or equal to $\left[ \frac{r}{2} \right]$, and use the estimate to show that for all odd prime $r$, if the holonomy group of the irreducible connection as above is simple and is not isomorphic to $E_8$, $F_4$, or $G_2$, then it is isomorphic to $SO(r)$.


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Additional Information

Jin-Hong Kim
Email: jinkim@math.berkeley.edu, jinkim@math.okstate.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05457-X
Received by editor(s): April 22, 1998
Published electronically: September 9, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society

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