6 papers · 1 filter
Homotopy types of fine curve and fine arc complexes
Ryan Dickmann, Zachary Himes, Alexander Nolte +1
The fine curve complex of a surface is a simplicial complex whose vertices are essential simple closed curves and whose -simplices are collections of disjoint curves. We p…
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…
Flexibility and degeneracy around a theorem of Thurston
Alexander Nolte
We give two flexible and degenerate constructions related to a theorem of Thurston. First, we produce geodesic segments for Thurston's asymmetric metric on Teichmüller space $\mat…
Concave Foliated Flag Structures and the Hitchin Component
Alexander Nolte, J. Maxwell Riestenberg
We give a geometric characterization of flag geometries associated to Hitchin representations in . Our characterization is based on distinguished invariant…
On Foliations in -Teichmüller Theory
Alexander Nolte
We carry out a detailed study of the structure of domains of discontinuity in of -Hitchin representations . We then prove the…
Metrics on Hitchin Components from Hölder Distortion
Alexander Nolte
We observe Thurston's asymmetric metric on Teichmüller space may be expressed in terms of the Hölder regularity of boundary maps. We then associate -dimensional stratified loc…