Morse and stable subgroups via the coset intersection complex
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866918419206504448 |
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| author | Fukaya, Tomohiro He, Haoyang Martínez-Pedroza, Eduardo Matsuka, Takumi |
| author_facet | Fukaya, Tomohiro He, Haoyang Martínez-Pedroza, Eduardo Matsuka, Takumi |
| contents | In this note, we study the equivalence of Morse and stable subgroups in the framework of the coset intersection complex. Under certain conditions on a coset intersection complex of a group, we prove that infinite-index Morse subgroups are stable. Our main theorem recovers results in the literature on right-angled Artin groups and graph products. As an application, we show that for the genus-two handlebody group, any infinite-index Morse subgroup is stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29158 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Morse and stable subgroups via the coset intersection complex Fukaya, Tomohiro He, Haoyang Martínez-Pedroza, Eduardo Matsuka, Takumi Group Theory In this note, we study the equivalence of Morse and stable subgroups in the framework of the coset intersection complex. Under certain conditions on a coset intersection complex of a group, we prove that infinite-index Morse subgroups are stable. Our main theorem recovers results in the literature on right-angled Artin groups and graph products. As an application, we show that for the genus-two handlebody group, any infinite-index Morse subgroup is stable. |
| title | Morse and stable subgroups via the coset intersection complex |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.29158 |