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Sungwoon Kim

Publications and source records attributed to Sungwoon Kim.

23 records · Page 2Linked to original sources
arXiv2012

Volume invariant and maximal representations of discrete subgroups of Lie groups

Let $Γ$ 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 $Γ$ 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 $Γ$ into $G$ except for $Γ\subset \mathrm{PSL_2 \mathbb{C}}$ a nonuniform lattice.

math.GT↗
arXiv2012

Proportionality principle for the simplicial volume of families of Q-rank 1 locally symmetric spaces

We establish the proportionality principle between the Riemannian volume and locally finite simplicial volume for Q-rank 1 locally symmetric spaces covered by products of hyperbolic spaces, giving the first examples for manifolds whose cusp groups are not necessarily amenable. Also, we give a simple direct proof of the proportionality principle for the locally finite simplicial volume and the relative simplicial volume of Q-rank 1 locally symmetric spaces with amenable cusp groups established by Löh and Sauer.

math.GT↗
arXiv2011

Bounded cohomology and negatively curved manifolds

We study the bounded fundamental class in the top dimensional bounded cohomology of negatively curved manifolds with infinite volume. We prove that the bounded fundamental class of $M$ vanishes if $M$ is geometrically finite. Furthermore, when $M$ is a $\mathbb{R}$-rank one locally symmetric space, we show that the bounded fundamental class of $M$ vanishes if and only if the Riemannian volume form on $M$ is the differential of a bounded differential form on $M$.

math.GT↗