1 citations · 2 across the 15 of their papers we have counts for
20 papers
The Thurston spine and equivariant cell decompositions in genus 2
Ni An, Jiexing Chen, Ingrid Irmer +1
The Thurston spine of the genus 2 Teichmüller space of closed compact surfaces is obtained. In particular, we identify all mapping class group-orbits of filling sets of systoles in…
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…
Explicit generators of the Steinberg Module of the mapping class group
Ingrid Irmer
A conjecture of Broaddus is proven, giving a simple characterisation of a representative of the unique orbit of the action of the mapping class group on the homology of Harvey's co…
Small Systle Sets and Coxeter Groups
Ingrid Irmer, Olivier Mathieu
The systoles of a hyperbolic surface Σ are the shortest closed geodesics. We say that the systoles fill the surface if the set Syst(Σ) of all systoles cuts Σ into polygons. We refi…
An equivariant deformation retraction of the Thurston spine
Ingrid Irmer
This paper shows that there is a mapping class group-equivariant deformation retraction of the Teichmüller space of a closed, orientable surface onto a cell complex of dimension eq…
The twist-cofinite topology on the mapping class group of a surface
Ingrid Irmer
A topology is defined on the mapping class group of a compact connected orientable surface. It is shown that a notion of "genericity" on subsets of the mapping class group arises f…
Finding simple curves in surface covers is undecidable
Ingrid Irmer
It is shown that various questions about the existence of simple closed curves in normal subgroups of surface groups are undecidable.
Examples of covering properties of boundary points of space-times
Ingrid Irmer
The problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whet…
Lifts of simple curves in finite regular coverings of closed surfaces
Ingrid Irmer
Suppose is a closed orientable surface and is a finite sheeted regular cover of . The following question was posed by Julién Marché in Mathoverflow: Do the lifts…
Fibering rigidity of 3-manifolds with Torelli monodromy
Ingrid Irmer
In this paper it is proven that there is at most one way, up to isotopy, in which a connected, hyperbolic, orientable 3-manifold can fiber over the circle with monodromy in the Tor…
Stable Lengths on the pants graph are rational
Ingrid Irmer
For the pants graph, there is little known about the behaviour of geodesics, as opposed to quasigeodesics. Brock-Masur-Minsky showed that geodesics or geodesic segments connecting…
The Chillingworth Class is a Signed Stable Length
Ingrid Irmer
An orientation is defined on a family of curve graphs on which the Torelli group acts. It is shown that the resulting signed stable length of an element of the Torelli group is a c…
Critical levels and Jacobi fields in a complex of cycles
Ingrid Irmer
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is def…
A Curve Complex and Incompressible Surfaces in
Ingrid Irmer
Various curve complexes with vertices representing multicurves on a surface have been defined, for example [3], [4] and [8]. The homology curve complex defi…
Geometry of the Homology Curve Complex
Ingrid Irmer
Suppose is a closed, oriented surface of genus at least two. This paper investigates the geometry of the homology multicurve complex, , of ; a complex clo…