On polynomial free-by-cyclic groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910757099143168 |
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| author | Mutanguha, Jean Pierre |
| author_facet | Mutanguha, Jean Pierre |
| contents | A free-by-cyclic group can often be viewed as a mapping torus of a free group automorphism (monodromy) in multiple ways. What dynamical properties must these monodromies share, and to what extent are they invariant under quasi-isometries? We give a new proof using cyclic splittings that the growth type of a monodromy is a geometric invariant of the free-by-cyclic group; we also characterise the degree of polynomial growth using slender splittings. For exponential growth, we conjecture that the nesting of attracting laminations is a geometric invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On polynomial free-by-cyclic groups Mutanguha, Jean Pierre Group Theory 20F65, 20E05, 20E36, 20E08 A free-by-cyclic group can often be viewed as a mapping torus of a free group automorphism (monodromy) in multiple ways. What dynamical properties must these monodromies share, and to what extent are they invariant under quasi-isometries? We give a new proof using cyclic splittings that the growth type of a monodromy is a geometric invariant of the free-by-cyclic group; we also characterise the degree of polynomial growth using slender splittings. For exponential growth, we conjecture that the nesting of attracting laminations is a geometric invariant. |
| title | On polynomial free-by-cyclic groups |
| topic | Group Theory 20F65, 20E05, 20E36, 20E08 |
| url | https://arxiv.org/abs/2412.16150 |