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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 ${\mathcal M}_{\mathcal C}$.
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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