Dynamics of the mapping class group on the moduli of a punctured sphere with rational holonomy
| dc.creator | Previte, Joseph P. | |
| dc.creator | Xia, Eugene Z. | |
| dc.date | 2003-11-21 | |
| dc.date.accessioned | 2026-07-07T05:03:08Z | |
| dc.date.available | 2026-07-07T05:03:08Z | |
| dc.description | Let $M$ be a four-holed sphere and $Γ$ the mapping class group of $M$ fixing the boundary $\partial M$. The group $Γ$ acts on $M_B(SL(2,C)) = Hom_B^+(pi_1(M),SL(2,C))/SL(2,C)$ which is the space of completely reducible $SL(2,C)$-gauge equivalence classes of flat $SL(2,C)$-connections on $M$ with fixed holonomy $B$ on $\partial M$. Let $B \in (-2,2)^4$ and $M_B$ be the compact component of the real points of $M_B(SL(2,C))$. These points correspond to SU(2)-representations or $SL(2,R)$-representations. The $Γ$-action preserves $M_B$ and we study the topological dynamics of the $Γ$-action on $M_B$ and show that for a dense set of holonomy $B \in (-2,2)^4$, the $Γ$-orbits are dense in $M_B$. We also produce a class of representations $ρ\in \Hom_B^+(pi_1(M),SL(2,R))$ such that the $Γ$-orbit of $[ρ]$ is finite in the compact component of $M_B(SL(2,R))$, but $ρ(π_1(M))$ is dense in $SL(2,R)$. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311373 | |
| dc.identifier | http://arxiv.org/abs/math/0311373 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69289 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 57M05; 54M20; 11D99 | |
| dc.title | Dynamics of the mapping class group on the moduli of a punctured sphere with rational holonomy | |
| dc.type | text |