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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.00346 |
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| _version_ | 1866915971942318080 |
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| author | Hillman, Jonathan A. |
| author_facet | Hillman, Jonathan A. |
| contents | We extend two results known for aspherical 3-manifolds to $PD_3$-pairs $(P,\partial{P})$ with aspherical ambient space $P$. Every such $PD_3$-pair may be assembled by attaching 1-handles to $PD_3$-pairs with aspherical; ambient space and $π_1$-injective boundary. (Thus the study of such pairs reduces to the study of $PD_3$-pairs of groups.) If $π$ is a group of type $FP$ whose indecomposable factors $G$ each have $χ(G_i)=0$ then there are only finitely many such $PD_3$-pairs with $π_1(P)\congπ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Aspherical $PD_3$-pairs Hillman, Jonathan A. Geometric Topology We extend two results known for aspherical 3-manifolds to $PD_3$-pairs $(P,\partial{P})$ with aspherical ambient space $P$. Every such $PD_3$-pair may be assembled by attaching 1-handles to $PD_3$-pairs with aspherical; ambient space and $π_1$-injective boundary. (Thus the study of such pairs reduces to the study of $PD_3$-pairs of groups.) If $π$ is a group of type $FP$ whose indecomposable factors $G$ each have $χ(G_i)=0$ then there are only finitely many such $PD_3$-pairs with $π_1(P)\congπ$. |
| title | Aspherical $PD_3$-pairs |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2605.00346 |