9 papers · 1 filter
The diameter function is a topological Morse function
Ingrid Irmer, Bhola Nath Saha
Schmutz Schaller developed techniques for studying Teichmüller space using the systole function. These were presented in \cite{SchmutzMorse}, \cite{SchmutzVoronoi} as a hyperbolic…
Understanding the well-rounded deformation retraction of Teichmüller space
Ingrid Irmer
In [10] it was shown that there is a mapping class group-equivariant deformation retraction of the Teichmüller space of a closed surface onto a CW complex with dimension equal to t…
Schmutz-Thurston Duality
Ingrid Irmer
Two people who pioneered the study of mapping class group-equivariant deformation retractions of Teichmüller space of closed compact surfaces are Schmutz Schaller and Thurston. Thi…
Existence and deformability of topological Morse functions
Ingrid Irmer
In the 1950s Morse defined the analogue of Morse functions for topological manifolds. In many instances, when mathematicians are using techniques on topological manifolds that appe…
Small genus, small index critical points of the systole function
Ni An, Ferdinand Ihringer, Ingrid Irmer
In this paper the index of a family of critical points of the systole function on Teichmüller space is calculated. The members of this family are interesting in that their existenc…
The Morse-Smale Property of the Thurston Spine
Ingrid Irmer
The Thurston spine consists of the subset of Teichmüller space at which the set of shortest curves, the systoles, cuts the surface into polygons. The systole function is a topologi…