Structured flow categories and twisted presheaves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910088617263104 |
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| author | Hedenlund, Alice Oldervoll, Trygve Poppe |
| author_facet | Hedenlund, Alice Oldervoll, Trygve Poppe |
| contents | An orientation theory for flow categories without bubbling is determined by a functor of $\infty$-categories $μ\colon \mathcal{C} \to U/O$. For any such functor, we construct a stable $\infty$-category $\mathcal{F}low^μ$ of $μ$-structured flow categories and bimodules. We also construct the expected functors between such $\infty$-categories, giving a tractable framework for manipulating orientations, local systems, and filtrations in exact Floer homotopy theory. Classifying spaces for certain bordism theories determined by $μ$ appear as mapping spaces in $\mathcal{F}low^μ$, and we use a Pontrjagin--Thom construction to naturally identify $\mathcal{F}low^μ$ with the $\infty$-category of $μ$-twisted presheaves on $\mathcal{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structured flow categories and twisted presheaves Hedenlund, Alice Oldervoll, Trygve Poppe Algebraic Topology Symplectic Geometry An orientation theory for flow categories without bubbling is determined by a functor of $\infty$-categories $μ\colon \mathcal{C} \to U/O$. For any such functor, we construct a stable $\infty$-category $\mathcal{F}low^μ$ of $μ$-structured flow categories and bimodules. We also construct the expected functors between such $\infty$-categories, giving a tractable framework for manipulating orientations, local systems, and filtrations in exact Floer homotopy theory. Classifying spaces for certain bordism theories determined by $μ$ appear as mapping spaces in $\mathcal{F}low^μ$, and we use a Pontrjagin--Thom construction to naturally identify $\mathcal{F}low^μ$ with the $\infty$-category of $μ$-twisted presheaves on $\mathcal{C}$. |
| title | Structured flow categories and twisted presheaves |
| topic | Algebraic Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2603.29576 |