Exceptional discrete mapping class group orbits in moduli spaces

Joseph P. Previte; Eugene Z. Xia

doi:10.1515/form.2003.048

Exceptional discrete mapping class group orbits in moduli spaces

Joseph P. Previte, Eugene Z. Xia

School of Science (Behrend)

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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 _ℬ(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_ℬ(SU(2)), This phenomenon does not occur for surfaces with genus greater than zero.

Original language	English (US)
Pages (from-to)	949-954
Number of pages	6
Journal	Forum Mathematicum
Volume	15
Issue number	6
DOIs	https://doi.org/10.1515/form.2003.048
State	Published - 2003

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/form.2003.048

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AB - 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 ℬ(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 ℳℬ(SU(2)), This phenomenon does not occur for surfaces with genus greater than zero.

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Exceptional discrete mapping class group orbits in moduli spaces

Abstract

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