Microlocal categories over Novikov rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916283743731712 |
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| author | Ike, Yuichi Kuwagaki, Tatsuki |
| author_facet | Ike, Yuichi Kuwagaki, Tatsuki |
| contents | In this paper, we define a family of categories for each Liouville manifold, which is an enhanced version of the category first introduced by Tamarkin. Using our categories, for any (possibly non-exact immersed) Lagrangian brane, we develop a theory of sheaf quantization generalizing the previous researches. In particular, our theory involves the notion of a sheaf-theoretic bounding cochain, which is a conjectural counterpart of the theory of Fukaya--Oh--Ohta--Ono. We also study several structures of our categories for sufficiently Weinstein manifolds and properties known in the classical Tamarkin category; intersection points estimates, interleaving distances, energy stability with respect to Guillermou--Kashiwara--Schapira autoequivalence, and the completeness of the distance. We conjecture that our category is equivalent to a Fukaya category defined over the Novikov ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01561 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Microlocal categories over Novikov rings Ike, Yuichi Kuwagaki, Tatsuki Symplectic Geometry In this paper, we define a family of categories for each Liouville manifold, which is an enhanced version of the category first introduced by Tamarkin. Using our categories, for any (possibly non-exact immersed) Lagrangian brane, we develop a theory of sheaf quantization generalizing the previous researches. In particular, our theory involves the notion of a sheaf-theoretic bounding cochain, which is a conjectural counterpart of the theory of Fukaya--Oh--Ohta--Ono. We also study several structures of our categories for sufficiently Weinstein manifolds and properties known in the classical Tamarkin category; intersection points estimates, interleaving distances, energy stability with respect to Guillermou--Kashiwara--Schapira autoequivalence, and the completeness of the distance. We conjecture that our category is equivalent to a Fukaya category defined over the Novikov ring. |
| title | Microlocal categories over Novikov rings |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2307.01561 |