Ergodicity of mapping class group actions on representation varieties, I. Closed surfaces

By D. Pickrell, Eugene Z. Xia. 2000

51 citations recorded by the source corpus.

Abstract. We prove that the mapping class group of a closed surface acts ergodically on connected components of the representation variety corresponding to a connected compact Lie group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f8e5c15b700e5d8c975c5ac567cdb15026a8d1a

How researchers see this paper

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In Geometry and Topology

1. William M. Goldman
2. Tudor Dimofte
3. Sergei Gukov
4. Ludovic Marquis

In Mathematical Physics

1. William M. Goldman
2. Sergei Gukov
3. Tudor Dimofte
4. Ludovic Marquis

Citations in the corpus

• The complex-symplectic geometry of SL(2,C)-characters over surfaces (2003, background): “By [15] and Pickrell-Xia [38], the resulting measure is ergodic under Γ when G is a compact Lie group.”
• MAPPING CLASS GROUP DYNAMICS ON SURFACE GROUP REPRESENTATIONS (2005, background): “For general G, this theorem is due to Pickrell-Xia [79] when Σ is closed and orientable, and Pickrell-Xia [80] for compact orientable surfaces of positive genus.”