Loop spaces of $n$-dimensional Poincaré duality complexes whose $(n-1)$-skeleton is a co-$H$-space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912431116124160 |
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| author | Stanton, Lewis Theriault, Stephen |
| author_facet | Stanton, Lewis Theriault, Stephen |
| contents | Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension $n$ whose $(n-1)$-skeleton is a co-$H$-space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincaré Duality complex retracts off the loops of its $(n-1)$-skeleton and describe its homology as a one-relator algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loop spaces of $n$-dimensional Poincaré duality complexes whose $(n-1)$-skeleton is a co-$H$-space Stanton, Lewis Theriault, Stephen Algebraic Topology Primary 55P35, 57R19 Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension $n$ whose $(n-1)$-skeleton is a co-$H$-space. This unifies many known decompositions obtained in different contexts and establishes many new families of examples. As consequences, we show that such a looped Poincaré Duality complex retracts off the loops of its $(n-1)$-skeleton and describe its homology as a one-relator algebra. |
| title | Loop spaces of $n$-dimensional Poincaré duality complexes whose $(n-1)$-skeleton is a co-$H$-space |
| topic | Algebraic Topology Primary 55P35, 57R19 |
| url | https://arxiv.org/abs/2502.15385 |