An equivariant deformation retraction of the Thurston spine
Abstract
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.
Keywords
Cite
@article{arxiv.2211.03429,
title = {An equivariant deformation retraction of the Thurston spine},
author = {Ingrid Irmer},
journal= {arXiv preprint arXiv:2211.03429},
year = {2025}
}
Comments
This paper was split into 3 pieces. The survey of Thurston's work is here "Thurston's deformation retraction of Teichm\"uller Space'', to appear in "In the Tradition of Thurston IV'' the second is "A matroid property of filling curves'' to appear in "Bulletin of the Australian Mathematical Society''. This version corresponds to the final chapter of the original paper