Property (T) and Poincaré duality in dimension three
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915761046421504 |
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| author | Rudd, Cameron Gates |
| author_facet | Rudd, Cameron Gates |
| contents | We use a recent result of Bader and Sauer on coboundary expansion to prove residually finite three-dimensional Poincaré duality groups never have property (T). This implies such groups are never Kähler. The argument applies to fundamental groups of (possibly non-aspherical) compact 3-manifolds, giving a new proof of a theorem of Fujiwara that states if the fundamental group of a compact 3-manifold has property (T), then that group is finite. The only consequence of geometrization needed in the proof is that 3-manifold groups are residually finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Property (T) and Poincaré duality in dimension three Rudd, Cameron Gates Geometric Topology Group Theory We use a recent result of Bader and Sauer on coboundary expansion to prove residually finite three-dimensional Poincaré duality groups never have property (T). This implies such groups are never Kähler. The argument applies to fundamental groups of (possibly non-aspherical) compact 3-manifolds, giving a new proof of a theorem of Fujiwara that states if the fundamental group of a compact 3-manifold has property (T), then that group is finite. The only consequence of geometrization needed in the proof is that 3-manifold groups are residually finite. |
| title | Property (T) and Poincaré duality in dimension three |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2512.24919 |