The mapping class group action on -character varieties-Reference-Cited by-同舟云学术

The mapping class group action on -character varieties

Published:2020-06-15 Issue:8 Volume:41 Page:2382-2396
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

GOLDMAN WILLIAM M.^ORCID,LAWTON SEAN^ORCID,XIA EUGENE Z.^ORCID

Abstract

AbstractLet

$\unicode[STIX]{x1D6F4}$

be a compact orientable surface of genus

$g=1$

with

$n=1$

boundary component. The mapping class group

$\unicode[STIX]{x1D6E4}$

$\unicode[STIX]{x1D6F4}$

acts on the

$\mathsf{SU}(3)$

-character variety of

$\unicode[STIX]{x1D6F4}$

. We show that the action is ergodic with respect to the natural symplectic measure on the character variety.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference20 articles.

1. [Law06] Lawton, S. . $\text{SL}(3,\text{C})$ -character varieties and RP2-structures on a trinion. PhD Thesis, University of Maryland, College Park, ProQuest LLC, Ann Arbor, MI, 2006.

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

3. An Introduction to Ergodic Theory

4. The symplectic nature of fundamental groups of surfaces

5. Lie Groups and Algebraic Groups

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