PreprintarXiv licencearXiv
The derived Picard group of Fukaya categories of closed surfaces
Abstract
Let Σg be a closed oriented surface of genus g≥2, and let ℱg be its split-closed, strictly unobstructed, two-periodic Fukaya category over the complex Novikov field Λ. We determine the derived Picard group DPicΛ(ℱg) ≅ (H1(Σg;Λ×) rtimesπ0Diff+(Σg)) ×ℤ/2ℤ. This proves the enhanced form of the conjecture of arXiv:2006.09689. As a corollary, we obtain that the derived Picard group itself determines the genus of the surface.
Related
BibTeX
@misc{wu2026derived,
title = {{The derived Picard group of Fukaya categories of closed surfaces}},
author = {Dongjian Wu and Nantao Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37403},
eprint = {2609.37403},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37403},
}
RIS
TY - UNPB
TI - The derived Picard group of Fukaya categories of closed surfaces
AU - Dongjian Wu
AU - Nantao Zhang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37403
UR - https://arxiv.org/abs/2609.37403
AB - Let Σ_g be a closed oriented surface of genus g≥2, and let ℱ_g be its split-closed, strictly unobstructed, two-periodic Fukaya category over the complex Novikov field Λ. We determine the derived Picard group DPic_Λ(ℱ_g) ≅ (H^1(Σ_g;Λ^×) rtimesπ_0Diff^+(Σ_g)) ×ℤ/2ℤ. This proves the enhanced form of the conjecture of arXiv:2006.09689. As a corollary, we obtain that the derived Picard group itself determines the genus of the surface.
ER -