Unipotent linear suspensions of free groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909231292088320 |
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| author | Dahmani, François Touikan, Nicholas |
| author_facet | Dahmani, François Touikan, Nicholas |
| contents | Motivated by the study of the conjugacy problem for outer automorphism of free groups, we develop the algorithmic theory of the free-by-cyclic group produced by unipotent linearly growing automorphisms of f.g. free groups.
We compute canonical splittings of these suspensions as well as their subgroups. We compute their automorphism groups. We show that this class of suspensions is effectively coherent. We solve the mixed Whitehead problem in these suspensions and show that their subgroups all satisfy the Minkowski property, i.e. that torsion in their outer automorphism group is faithfully represented in some computable finite quotients.
An application of our results is a solution to the conjugacy problem for outer automorphisms of free groups whose polynomially growing part is unipotent linear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11274 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unipotent linear suspensions of free groups Dahmani, François Touikan, Nicholas Group Theory 20F28, 20E36, 20E05, 20E06 Motivated by the study of the conjugacy problem for outer automorphism of free groups, we develop the algorithmic theory of the free-by-cyclic group produced by unipotent linearly growing automorphisms of f.g. free groups. We compute canonical splittings of these suspensions as well as their subgroups. We compute their automorphism groups. We show that this class of suspensions is effectively coherent. We solve the mixed Whitehead problem in these suspensions and show that their subgroups all satisfy the Minkowski property, i.e. that torsion in their outer automorphism group is faithfully represented in some computable finite quotients. An application of our results is a solution to the conjugacy problem for outer automorphisms of free groups whose polynomially growing part is unipotent linear. |
| title | Unipotent linear suspensions of free groups |
| topic | Group Theory 20F28, 20E36, 20E05, 20E06 |
| url | https://arxiv.org/abs/2305.11274 |