When is the Outer Space of a free product CAT(0)?
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915238438240256 |
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| author | Lyman, Robert Alonzo |
| author_facet | Lyman, Robert Alonzo |
| contents | Generalizing Culler and Vogtmann's Outer Space for the free group, Guirardel and Levitt construct an Outer Space for a free product of groups. We completely characterize when this space (or really its simplicial spine) supports an equivariant piecewise-Euclidean or piecewise-hyperbolic CAT(0) metric. Our results are mostly negative, extending thesis work of Bridson and related to thesis work of Cunningham. In particular, provided the dimension of the spine is at least three, it is never CAT(0). Surprisingly, we exhibit one family of free products for which the Outer Space is two-dimensional and does support an equivariant CAT(0) metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_04711 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | When is the Outer Space of a free product CAT(0)? Lyman, Robert Alonzo Group Theory 20F65, 20E08, 20F67 Generalizing Culler and Vogtmann's Outer Space for the free group, Guirardel and Levitt construct an Outer Space for a free product of groups. We completely characterize when this space (or really its simplicial spine) supports an equivariant piecewise-Euclidean or piecewise-hyperbolic CAT(0) metric. Our results are mostly negative, extending thesis work of Bridson and related to thesis work of Cunningham. In particular, provided the dimension of the spine is at least three, it is never CAT(0). Surprisingly, we exhibit one family of free products for which the Outer Space is two-dimensional and does support an equivariant CAT(0) metric. |
| title | When is the Outer Space of a free product CAT(0)? |
| topic | Group Theory 20F65, 20E08, 20F67 |
| url | https://arxiv.org/abs/2209.04711 |