Chain duality for categories over complexes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913181238034432 |
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| author | Davis, James F. Rovi, Carmen |
| author_facet | Davis, James F. Rovi, Carmen |
| contents | We show that the additive category of chain complexes parametrized by a finite simplicial complex $K$ forms a category with chain duality. This fact, never fully proven in the original reference, is fundamental for Ranicki's algebraic formulation of the surgery exact sequence of Sullivan and Wall, and his interpretation of the surgery obstruction map as the passage from local Poincaré duality to global Poincaré duality. Our paper also gives a new, conceptual, and geometric treatment of chain duality on $K$-based chain complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_01946 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chain duality for categories over complexes Davis, James F. Rovi, Carmen Algebraic Topology Category Theory Geometric Topology K-Theory and Homology 57M05 We show that the additive category of chain complexes parametrized by a finite simplicial complex $K$ forms a category with chain duality. This fact, never fully proven in the original reference, is fundamental for Ranicki's algebraic formulation of the surgery exact sequence of Sullivan and Wall, and his interpretation of the surgery obstruction map as the passage from local Poincaré duality to global Poincaré duality. Our paper also gives a new, conceptual, and geometric treatment of chain duality on $K$-based chain complexes. |
| title | Chain duality for categories over complexes |
| topic | Algebraic Topology Category Theory Geometric Topology K-Theory and Homology 57M05 |
| url | https://arxiv.org/abs/2204.01946 |