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arXiv · 2307.01561

Microlocal categories over Novikov rings

Yuichi Ike·Tatsuki Kuwagaki
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Abstract

In this paper, we define a family of categories for each Weinstein 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.

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Yuichi Ike, Tatsuki Kuwagaki. 2023-07-04. Microlocal categories over Novikov rings. https://arxiv.org/abs/2307.01561

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