Triangulation, Persistence, and Fukaya categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916351662096384 |
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| author | Biran, Paul Cornea, Octav Zhang, Jun |
| author_facet | Biran, Paul Cornea, Octav Zhang, Jun |
| contents | This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of morphisms of such a TPC are persistence modules and this category is endowed with a class of weighted distinguished triangles. Under favourable conditions we show that the derived Fukaya category admits a TPC refinement and this is applied to deduce a global rigidity result for spaces of compact, exact Lagrangians in certain Liouville manifolds: we construct a metric on this space with intrinsic symplectic properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01785 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Triangulation, Persistence, and Fukaya categories Biran, Paul Cornea, Octav Zhang, Jun Symplectic Geometry Algebraic Topology 53D37, 55N31 (Primary), 53D12 (Secondary) This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of morphisms of such a TPC are persistence modules and this category is endowed with a class of weighted distinguished triangles. Under favourable conditions we show that the derived Fukaya category admits a TPC refinement and this is applied to deduce a global rigidity result for spaces of compact, exact Lagrangians in certain Liouville manifolds: we construct a metric on this space with intrinsic symplectic properties. |
| title | Triangulation, Persistence, and Fukaya categories |
| topic | Symplectic Geometry Algebraic Topology 53D37, 55N31 (Primary), 53D12 (Secondary) |
| url | https://arxiv.org/abs/2304.01785 |