Shifted Symplectic Fibrations and Derived Thurston Theorem
Abstract
In classical symplectic geometry, under mild conditions, Thurston proved that one can construct a compatible symplectic form on the total space of a symplectic fibration with a connected symplectic base. Here we prove a derived symplectic analogue of this result, called the derived Thurston theorem. More precisely, we show that if a morphism π: X → S of derived stacks has a shifted symplectic fibration structure and the target stack S admits a shifted symplectic structure, then, under certain conditions, one can construct a shifted symplectic structure on a dense Zariski-open derived substack of the source stack X, compatible with π in a sense similar to the classical case. In this derived setting, we also present numerous examples of shifted symplectic fibrations, develop an affine model construction for such fibrations, and provide applications of the derived Thurston theorem.
Related
- Shifted Contact Structures on Exact Symplectic Fibrations
- The shifted symplectic geometry of derived higher groupoids
- Equivariant Quotients of Derived Symplectic Spaces and Legendrian Intersection Theorem
- Gurtas Lefschetz Fibrations, Rational Blowdowns, and Exotic Symplectic Four-Manifolds
- Degenerations of shifted symplectic moduli stacks of sheaves
BibTeX
@misc{arıkan2026shifted,
title = {{Shifted Symplectic Fibrations and Derived Thurston Theorem}},
author = {Mehmet Fırat Arıkan and Kadri İlker Berktav and Efe İzbudak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.21717},
eprint = {2606.21717},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21717},
}
RIS
TY - UNPB
TI - Shifted Symplectic Fibrations and Derived Thurston Theorem
AU - Mehmet Fırat Arıkan
AU - Kadri İlker Berktav
AU - Efe İzbudak
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2606.21717
UR - https://arxiv.org/abs/2606.21717
AB - In classical symplectic geometry, under mild conditions, Thurston proved that one can construct a compatible symplectic form on the total space of a symplectic fibration with a connected symplectic base. Here we prove a derived symplectic analogue of this result, called the derived Thurston theorem. More precisely, we show that if a morphism π: X → S of derived stacks has a shifted symplectic fibration structure and the target stack S admits a shifted symplectic structure, then, under certain conditions, one can construct a shifted symplectic structure on a dense Zariski-open derived substack of the source stack X, compatible with π in a sense similar to the classical case. In this derived setting, we also present numerous examples of shifted symplectic fibrations, develop an affine model construction for such fibrations, and provide applications of the derived Thurston theorem.
ER -