The spine which was no spine

2007/05/01 by Alexandra Pettet, Pettet, Alexandra, Juan Souto +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #math.GT

paper · pdf · doi:10.48550/arxiv.0705.0170

arxiv created 2007/05/01 · openalex publication_date 2007/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T_n be the Teichmueller space of flat metrics on the n-dimensional torus and identify SL(n,Z) with the corresponding mapping class group. We prove that the subset Y consisting of those points at which the systoles generate the fundamental group of the torus is, for n > 4, not contractible. In particular, Y is not an SL(n,Z)-equivariant deformation retract of T_n.

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