Fixed points of the mapping class group

in the moduli spaces

Author:
Jørgen Ellegaard Andersen

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1511-1515

MSC (1991):
Primary 53C07

DOI:
https://doi.org/10.1090/S0002-9939-97-03788-X

MathSciNet review:
1376748

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a compact oriented surface with or without boundary components. In this note we prove that if then there exist infinitely many integers such that there is a point in the moduli space of irreducible flat connections on which is fixed by any orientation preserving diffeomorphism of . Secondly we prove that for each orientation preserving diffeomorphism of and each there is some such that has a fixed point in the moduli space of irreducible flat connections on . Thirdly we prove that for all there exists an integer such that the 'th power of any diffeomorphism fixes a certain point in the moduli space of irreducible flat connections on .

**1.**J. E. Andersen, The Witten Invariant of finite order mapping tori I.,*University of Aarhus, Department of Mathematics Preprint*(1995-21)**2.**C.D. Frohman, Unitary Representations of knot groups,*Topology*32 (1993) 121-144 MR**94g:57003****3.**C.D. Frohman & D.D. Long, Casson's invariant and surgery on knots,*Procedings of the Edinburg Mathmatical Society*35 (1992) 383-395 MR**94a:57012****4.**W. Fulton & J. Harris, Representation Theory, A first course.,*Springer Graduate Texts in Mathematics*, Springer-Verlag, 1991 MR**93a:20069****5.**S. Lang, Algebra,*Addison-Wesley 1984.*MR**86j:00003**

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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:
https://doi.org/10.1090/S0002-9939-97-03788-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