Topological rigidity of closures of certain sparse unipotent orbits in finite-volume quotients of $\prod_{i=1}^k\operatorname{SL}_2(\mathbb R)$

TL;DR

This paper provides a straightforward proof of topological rigidity for closures of specific sparse unipotent orbits in finite-volume quotients of a product of SL(2,R) groups, contributing to the understanding of orbit structure in homogeneous spaces.

Contribution

It introduces a simple proof establishing topological rigidity for certain unipotent orbit closures in products of SL(2,R) quotients, advancing the theory of homogeneous dynamics.

Findings

Proof of topological rigidity for unipotent orbit closures

Clarification of orbit closure structures in product spaces

Enhanced understanding of dynamics in homogeneous spaces

Abstract

We give a simple proof about the topological rigidity of closures of certain sparse unipotent orbits in $G/\Gamma$ where $G=\prod_{i=1}^k\operatorname{SL}_2(\mathbb R)$ and $\Gamma$ is an irreducible lattice in $G$.