Fixed points of the mapping class group in the $SU(n)$ moduli spaces
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- by Jørgen Ellegaard Andersen PDF
- Proc. Amer. Math. Soc. 125 (1997), 1511-1515 Request permission
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 $\Sigma$.References
- J. E. Andersen, The Witten Invariant of finite order mapping tori I., University of Aarhus, Department of Mathematics Preprint (1995–21)
- Charles Frohman, Unitary representations of knot groups, Topology 32 (1993), no. 1, 121–144. MR 1204411, DOI 10.1016/0040-9383(93)90042-T
- C. D. Frohman and D. D. Long, Casson’s invariant and surgery on knots, Proc. Edinburgh Math. Soc. (2) 35 (1992), no. 3, 383–395. MR 1187001, DOI 10.1017/S0013091500005678
- William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249, DOI 10.1007/978-1-4612-0979-9
- Serge Lang, Algebra, 2nd ed., Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1984. MR 783636
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
- 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
- © Copyright 1997 American Mathematical Society
- 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