TL;DR
This paper demonstrates that a previously proposed proper action of a surface group on a product of trees is actually not proper, clarifying the nature of such group actions.
Contribution
It provides a counterexample to the claim that the action is proper, refining understanding of surface group actions on products of trees.
Findings
The action of the surface group is not proper.
Clarifies limitations of previous constructions.
Contributes to the theory of group actions on trees.
Abstract
In 1999, Long and Reid proposed a proper action of a surface group on a product of trees. In this note, we show that the action is not proper.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology