Topological dynamics on moduli spaces II
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- by Joseph P. Previte and Eugene Z. Xia PDF
- Trans. Amer. Math. Soc. 354 (2002), 2475-2494 Request permission
Abstract:
Let $M$ be an orientable genus $g>0$ surface with boundary $\partial M$. Let $\Gamma$ be the mapping class group of $M$ fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \operatorname {Hom}_{\mathcal C}(\pi _1(M),\operatorname {SU})/\operatorname {SU},$ the space of $\operatorname {SU}$-gauge equivalence classes of flat $\operatorname {SU}$-connections on $M$ with fixed holonomy on $\partial M$. We study the topological dynamics of the $\Gamma$-action and give conditions for the individual $\Gamma$-orbits to be dense in ${\mathcal M}_{\mathcal C}$.References
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Additional Information
- Joseph P. Previte
- Affiliation: School of Science, Penn State University Erie, The Behrend College, Erie, Pennsylvania 16563
- Email: jpp@vortex.bd.psu.edu
- Eugene Z. Xia
- Affiliation: Department of Mathematics & Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515
- Email: xia@math.umass.edu
- Received by editor(s): September 26, 2000
- Received by editor(s) in revised form: June 28, 2001
- Published electronically: February 1, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 2475-2494
- MSC (2000): Primary 57M05, 54H20
- DOI: https://doi.org/10.1090/S0002-9947-02-02961-6
- MathSciNet review: 1885660