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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2506.11228 |
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| _version_ | 1866908406356377600 |
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| author | Plummer, Maxwell |
| author_facet | Plummer, Maxwell |
| contents | Given a splitting of a free-by-cyclic group, the associated monodromy acts on outer space preserving Handel and Mosher's "axis bundle." We show that the property of a monodromy having a "lone axis" is non-generic in the sense that the associated splittings are projectively discrete in first cohomology. Additionally, we show that this discreteness statement cannot be promoted to a finiteness statement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Axis bundles in free-by-cyclic groups Plummer, Maxwell Group Theory Geometric Topology Given a splitting of a free-by-cyclic group, the associated monodromy acts on outer space preserving Handel and Mosher's "axis bundle." We show that the property of a monodromy having a "lone axis" is non-generic in the sense that the associated splittings are projectively discrete in first cohomology. Additionally, we show that this discreteness statement cannot be promoted to a finiteness statement. |
| title | Axis bundles in free-by-cyclic groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2506.11228 |