arXiv subjects

Son Lam Ho

Publications and source records attributed to Son Lam Ho.

2 recordsLinked to original sources

arXiv2016

Deformations of fundamental group representations and earthquakes on $SO(n,1)$ surface groups

In this article we construct a type of deformations of representations $π_1(M)\rightarrow G$ where $G$ is an arbitrary lie group and $M$ is a large class of manifolds including CAT(0) manifolds. The deformations are defined based on codimension 1 hypersurfaces with certain conditions, and also on disjoint union of such hypersurfaces, i.e. multi-hypersurfaces. We show commutativity of deforming along disjoint hypersurfaces. As application, we consider Anosov surface groups in $SO(n,1)$ and show that the construction can be extended continuously to measured laminations, thus obtaining earthquake deformations on these surface groups.

math.GT↗

arXiv2014

On conformally flat circle bundles over surfaces

We study surface groups $Γ$ in $SO(4,1)$, which is the group of Mobius tranformations of $S^3$, and also the group of isometries of $\mathbb{H}^4$. We consider such $Γ$ so that its limit set $Λ_Γ$ is a quasi-circle in $S^3$, and so that the quotient $(S^3 - Λ_Γ) / Γ$ is a circle bundle over a surface. This circle bundle is said to be conformally flat, and our main goal is to discover how twisted such bundle may be by establishing a bound on its Euler number. By combinatorial approaches, we have two soft bounds in this direction on certain types of nice structures. In this article we also construct new examples, a "grafting" type path in the space of surface group representations into $SO(4,1)$: starting inside the quasi-Fuschsian locus, going through non-discrete territory and back.

math.GT↗