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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.04250 |
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| _version_ | 1866910856603762688 |
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| author | Iveson, Harry |
| author_facet | Iveson, Harry |
| contents | We give a concise presentation for the group of pure symmetric outer automorphisms of a given splitting of a free product $G_{1}\ast\dots\ast G_{n}$. These are the (outer) automorphisms which preserve the conjugacy classes of the free factors $G_{i}$. This is achieved by considering the action of these automorphisms on a particular subcomplex of `Outer Space', which we show to be simply connected. We then apply a theorem of K. S. Brown to extract our presentation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Presentation for the Group of Pure Symmetric Outer Automorphisms of a Given Splitting of a Free Product Iveson, Harry Group Theory We give a concise presentation for the group of pure symmetric outer automorphisms of a given splitting of a free product $G_{1}\ast\dots\ast G_{n}$. These are the (outer) automorphisms which preserve the conjugacy classes of the free factors $G_{i}$. This is achieved by considering the action of these automorphisms on a particular subcomplex of `Outer Space', which we show to be simply connected. We then apply a theorem of K. S. Brown to extract our presentation. |
| title | A Presentation for the Group of Pure Symmetric Outer Automorphisms of a Given Splitting of a Free Product |
| topic | Group Theory |
| url | https://arxiv.org/abs/2412.04250 |