Shifted Contact Structures on Exact Symplectic Fibrations
Abstract
Within the framework of classical contact geometry, the first author introduced the notion of contact symplectic structure --the data of an exact symplectic fibration with a contact base-- and proved, under mild conditions, that the total space of such a fibration inherits a contact structure compatible with the fibration map, thereby establishing the contact Thurston theorem. This paper provides a derived contact version of that result by incorporating our prior work on the derived symplectic Thurston theorem. In this paper, we prove, under certain conditions, that if a morphism π: X → S of derived stacks has a shifted exact symplectic fibration structure and the target stack S admits a shifted contact structure, then one can construct a shifted contact structure on the source stack X, compatible with π in a sense similar to the smooth case. Our framework relies on the theory of relative shifted structures; hence our result, called the derived contact Thurston theorem, in fact establishes a relative-to-absolute type construction. As an application, we present examples of our relative-to-absolute construction formalism in the derived contact setting, including conormal stacks, quotient mapping stacks, and affine exact symplectic fibrations.
Related
- Shifted Symplectic Fibrations and Derived Thurston Theorem
- AKSZ Construction for Shifted Contact Structures
- Gurtas Lefschetz Fibrations, Rational Blowdowns, and Exotic Symplectic Four-Manifolds
- The shifted symplectic geometry of derived higher groupoids
- Degenerations of shifted symplectic moduli stacks of sheaves
BibTeX
@misc{arıkan2026shifted,
title = {{Shifted Contact Structures on Exact Symplectic Fibrations}},
author = {Mehmet Fırat Arıkan and Kadri İlker Berktav and Efe İzbudak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08617},
eprint = {2609.08617},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08617},
}
RIS
TY - UNPB
TI - Shifted Contact Structures on Exact Symplectic Fibrations
AU - Mehmet Fırat Arıkan
AU - Kadri İlker Berktav
AU - Efe İzbudak
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08617
UR - https://arxiv.org/abs/2609.08617
AB - Within the framework of classical contact geometry, the first author introduced the notion of contact symplectic structure --the data of an exact symplectic fibration with a contact base-- and proved, under mild conditions, that the total space of such a fibration inherits a contact structure compatible with the fibration map, thereby establishing the contact Thurston theorem. This paper provides a derived contact version of that result by incorporating our prior work on the derived symplectic Thurston theorem. In this paper, we prove, under certain conditions, that if a morphism π: X → S of derived stacks has a shifted exact symplectic fibration structure and the target stack S admits a shifted contact structure, then one can construct a shifted contact structure on the source stack X, compatible with π in a sense similar to the smooth case. Our framework relies on the theory of relative shifted structures; hence our result, called the derived contact Thurston theorem, in fact establishes a relative-to-absolute type construction. As an application, we present examples of our relative-to-absolute construction formalism in the derived contact setting, including conormal stacks, quotient mapping stacks, and affine exact symplectic fibrations.
ER -