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An equivariant deformation retraction of the Thurston spine

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arxiv 2211.03429 v5 pith:HB5GLP3A submitted 2022-11-07 math.GT math.GR

Ingrid Irmer This is my paper · ORCID
classification math.GTmath.GR
keywords thurstondeformationretractionspineclasscomplexdimensionmapping
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This paper shows that there is a mapping class group-equivariant deformation retraction of the Teichm\"uller space of a closed, orientable surface onto a cell complex of dimension equal to the virtual cohomological dimension of the mapping class group. The image of the deformation retraction is contained in the CW complex first described by Thurston -- the Thurston spine. The Thurston spine is the set of points in Teichm\"uller space corresponding to hyperbolic surfaces for which the set of shortest geodesics (the systoles) cuts the surface into polygons.

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  1. Understanding the well-rounded deformation retraction of Teichm\"uller space

    math.GT 2025-09 conditional novelty 6.0 of 10

    The author proves, modulo two of her own unpublished preprints, that Teichmüller space has a well-rounded, equivariant deformation retraction onto a complex of dimension 4g-5.

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