Conjugate -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 is and is an -subbundle of , the rank of the holonomy group of a connection which is gauge equivalent to its conjugate connection is less than or equal to , and use the estimate to show that for all odd prime , if the holonomy group of the *irreducible* connection as above is simple and is not isomorphic to , , or , then it is isomorphic to .

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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