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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fixed points of the mapping class group
in the $SU(n)$ moduli spaces


Author: Jørgen Ellegaard Andersen
Journal: Proc. Amer. Math. Soc. 125 (1997), 1511-1515
MSC (1991): Primary 53C07
MathSciNet review: 1376748
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Abstract: Let $\Sigma $ be a compact oriented surface with or without boundary components. In this note we prove that if $\chi (\Sigma ) < 0$ then there exist infinitely many integers $n$ such that there is a point in the moduli space of irreducible flat $SU(n)$ connections on $\Sigma $ which is fixed by any orientation preserving diffeomorphism of $\Sigma $. Secondly we prove that for each orientation preserving diffeomorphism $f$ of $\Sigma $ and each $n\ge 2$ there is some $m$ such that $f$ has a fixed point in the moduli space of irreducible flat $SU(n^m)$ connections on $\Sigma $. Thirdly we prove that for all $n\geq 2$ there exists an integer $m$ such that the $m$'th power of any diffeomorphism fixes a certain point in the moduli space of irreducible flat $SU(n)$ connections on $\Sigma $.


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Additional Information

Jørgen Ellegaard Andersen
Affiliation: Department of Mathematics, University of Aarhus, DK-8000 Aarhus, Denmark
Address at time of publication: Mathematical Sciences Research Institute, Berkeley, California 94720
Email: andersen@mi.aau.dk

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03788-X
PII: S 0002-9939(97)03788-X
Received by editor(s): November 17, 1995
Additional Notes: Supported in part by NSF grant DMS-93-09653, while the author was visiting the University of California, Berkeley
Communicated by: Ronald Stern
Article copyright: © Copyright 1997 American Mathematical Society