Fourier transforms and a filtration on the Lagrangian cobordism group of tori

Autor:	Muñiz-Brea, Álvaro
Rok vydání:	2024
Předmět:	Mathematics - Symplectic Geometry Mathematics - Algebraic Geometry 53D35 53D37 (Primary) 14C25 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Given a polarized tropical affine torus, we show that the fibered Lagrangian cobordism group of the corresponding symplectic manifold admits a natural geometric filtration of finite length. This contrasts with results of Sheridan-Smith in dimension four and the present author in higher dimensions, who showed that such group is infinite-dimensional. In the second half of this paper, we construct a Fourier transform between Fukaya categories of dual symplectic tori. We show that, under homological mirror symmetry, it corresponds to the Fourier transform between derived categories of coherent sheaves of dual abelian varieties due to Mukai. We use this to show how our filtration is mirror to the Bloch filtration on Chow groups of abelian varieties, but the results may be of broader interest. Comment: 36 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.16543 Zobrazit plný text záznamu View this record from Arxiv