Exceptional discrete mapping class group orbits in moduli spaces

Joseph P. Previte, Eugene Z. Xia

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Let M be a four-holed sphere and γ the mapping class group of M fixing ∂M. The group γ acts on the space ℳ (SU(2)) of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on ∂M. We give examples of flat SU(2)-connections whose holonomy groups are dense in SU(2), but whose γ-orbits are discrete in ℳ(SU(2)), This phenomenon does not occur for surfaces with genus greater than zero.

Original languageEnglish (US)
Pages (from-to)949-954
Number of pages6
JournalForum Mathematicum
Issue number6
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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