4 papers
Graphs of Quasicircles and Quasiconformal Homeomorphisms
Katherine Williams Booth, Alexander Nolte, Yvon Verberne
We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface of genus at least . In particular, we prove they are exa…
Automorphisms of smooth fine curve graphs
Katherine Williams Booth
In this paper, we consider the automorphisms of fine curve graphs restricted to continuously -differentiable curves. We show that for closed surfaces with genus at least 2, they…
A local characterization for homeomorphisms that preserve continuously differentiable curves
Katherine Williams Booth
We study the subgroup of the homeomorphism group consisting of homeomorphisms of a manifold that preserve the set of one-dimensional -submanifolds. For many surfaces, the simi…
Automorphisms of the fine 1-curve graph
Katherine Williams Booth, Daniel Minahan, Roberta Shapiro
The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show…