Eugene Z. Xia

activity

19992004

collaborators

Showing math.DSShow all

6 papers · 1 filter

math.DS2003

Dynamics of the mapping class group on the moduli of a punctured sphere with rational holonomy

Joseph P. Previte, Eugene Z. Xia

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 $M_{B} (S L (2, C)) = H o m_{B}^{+} (p i_{1} (M), S L (2, C)) / S L (2, C)$ whic…

math.DS2001

Exceptional Discrete Mapping Class Group Orbits in Moduli Spaces

Joseph P. Previte, Eugene Z. Xia

Let $M$ be a four-holed sphere and $Γ$ the mapping class group of $M$ fixing $\partial M$ . The group $Γ$ acts on the space $M_{B} (S U (2))$ of SU(2)-gauge equival…

math.DS2000

Ergodicity of Mapping Class Group Actions on Representation Varieties, II. Surfaces with Boundary

Doug Pickrell, Eugene Z. Xia

The mapping class group of a compact oriented surface of genus greater than one with boundary acts ergodically on connected components of the representation variety corresponding t…

math.DS2000

Ergodicity of Mapping Class Group Actions on Representation Varieties, I. Closed Surfaces

Doug Pickrell, Eugene Z. Xia

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.

math.DS1999

Topological Dynamics on Moduli Spaces, I

Joseph P. Previte, Eugene Z. Xia

Let M be a one-holed torus with boundary $\partial M$ (a circle) and $Γ$ the mapping class group of M fixing $\partial M$ . The group $Γ$ acts on $M_{C} (S U (2))$ …

math.DS1999

Topological Dynamics on Moduli Spaces II

Joseph P. Previte, Eugene Z. Xia

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $Γ$ be the mapping class group of M fixing $\partial M$ . The group $Γ$ acts on ${\mathcal M}_…