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Transactions of the American Mathematical Society

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Topological dynamics on moduli spaces II


Authors: Joseph P. Previte and Eugene Z. Xia
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
Published electronically: February 1, 2002
MathSciNet review: 1885660
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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 ${\mathcal M}_{\mathcal C} = \operatorname{Hom}_{\mathcal C}(\pi_1(M),\operatorname{SU}(2))/\operatorname{SU}(2),$ the space of $\operatorname{SU}(2)$-gauge equivalence classes of flat $\operatorname{SU}(2)$-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 ${\mathcal M}_{\mathcal C}$.


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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

DOI: https://doi.org/10.1090/S0002-9947-02-02961-6
Keywords: Fundamental group of a surface, mapping class group, Dehn twist, topological dynamics, moduli spaces
Received by editor(s): September 26, 2000
Received by editor(s) in revised form: June 28, 2001
Published electronically: February 1, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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