Inkang Kim
Volume invariant and maximal representations of discrete subgroups of Lie groups.
Wed, 05/23/2012 - 15:01 — SomNambulAuthors: Inkang Kim, Sungwoon Kim
Subjects: Geometric Topology
AbstractLet $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with
trivial center and no compact factors. We introduce a volume invariant for
representations of $\Gamma$ into $G$, which generalizes the volume invariant
for representations of uniform lattices introduced by Goldman. Then, we show
that the maximality of this volume invariant exactly characterizes discrete,
faithful representations of $\Gamma$ into $G$ except for $\Gamma\subset
\mathrm{PSL_2 \mathbb{C}}$ a nonuniform lattice.Flexibility of surface groups in classical groups.
Fri, 01/07/2011 - 16:01 — SomNambulAuthors: Inkang Kim, Pierre Pansu
Subjects: Differential Geometry
AbstractWe show that a surface group of high genus contained in a classical simple
Lie group can be deformed to become Zariski dense, unless the Lie group is
$SU(p,q)$ (resp. $SO^* (2n)$, $n$ odd) and the surface group is maximal in some
$S(U(p,p)\times U(q-p))\subset SU(p,q)$ (resp. $SO^* (2n-2)\times SO(2)\subset
SO^* (2n)$). This is a converse, for classical groups, to a rigidity result of
S. Bradlow, O. Garc\'{\i}a-Prada and P. Gothen.Primitive stable representations of geometrically infinite handlebody hyperbolic 3-manifolds.
Thu, 03/11/2010 - 16:01 — SomNambulAuthors: Woojin Jeon, Inkang Kim
Subjects: Geometric Topology
AbstractIn this paper, we answer Minsky's conjecture regarding primitive stable
representations affirmatively.
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