The boundary of bordified Outer space

2024/04/17 by Karen Vogtmann, Vogtmann, Karen · 1 citation
Physics and Astronomy · #20E36 #20F65 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Space exploration and regulation

paper · pdf · doi:10.48550/arxiv.2404.11371

openalex publication_date 2024/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundary of the "Jewel space" \mathcal J_n constructed in arXiv:1709.01296. This is an equivariant deformation retract of Outer space CV_n on which Out(F_n) acts properly and cocompactly, and is homeomorphic to the Bestvina-Feighn bordification of CV_n. In the current paper we analyze the structure of the boundary of \mathcal J_n. We then use the desctiption of the simplicial closure CV_n^* as the sphere complex of a connected sum of n copies of S¹× S² to prove that this boundary is homotopy equivalent to the subcomplex of CV_n^* spanned by vertices at infinity.

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