The boundary of bordified Outer space
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913994142384128 |
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| author | Vogtmann, Karen |
| author_facet | Vogtmann, Karen |
| contents | 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 $S^1\times S^2$ to prove that this boundary is homotopy equivalent to the subcomplex of $CV_n^*$ spanned by vertices at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The boundary of bordified Outer space Vogtmann, Karen Group Theory Geometric Topology 20E36, 20F65, 57M07 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 $S^1\times S^2$ to prove that this boundary is homotopy equivalent to the subcomplex of $CV_n^*$ spanned by vertices at infinity. |
| title | The boundary of bordified Outer space |
| topic | Group Theory Geometric Topology 20E36, 20F65, 57M07 |
| url | https://arxiv.org/abs/2404.11371 |