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Mathematische Zeitschrift

, Volume 240, Issue 1, pp 95–109 | Cite as

The moduli of flat PU(p,p)-structures with large Toledo invariants

  • E. Markman
  • E.Z. Xia
Original article

Abstract.

For a compact Riemann surface X of genus \(g > 1, {\rm Hom}(\pi_1(X),{\rm PU}(p,q))/{\rm PU}(p,q)\) is the moduli space of flat \({\rm PU}(p,q)\)-connections on X. There are two invariants, the Chern class c and the Toledo invariant \(\tau\) associated with each element in the moduli. The Toledo invariant is bounded in the range \(-2min(p,q)(g-1) \le \tau \le 2min(p,q)(g-1)\). This paper shows that the component, associated with a fixed \(\tau > 2(max(p,q)-1)(g-1)\) (resp. \(\tau < -2(max(p,q)-1)(g-1)\)) and a fixed Chern class c, is connected (The restriction on \(\tau\) implies p=q).

Mathematics Subject Classification (1991): 14D20, 14H60 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • E. Markman
    • 1
  • E.Z. Xia
    • 1
  1. 1.Department of Mathematics, University of Massachusetts, Amherst, MA 01003-4515, USA (e-mail: markman@math.umass.edu,xia@math.umass.edu) US

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