On some rigidity results for high-dimensional confoliations
Abstract
The main result is an obstruction to the presence of contact regions for c-symplectic confoliations in any odd ambient dimension. As a first application, we prove a 5-dimensional analogue (under stronger assumptions) of a Reeb stability theorem for confoliations in dimension 3 due to Eliashberg and Thurston. Refining work of the first author with Cardona, we further give two new notions of contact approximations of c-symplectic confoliations in any odd ambient dimension generalizing the 3-dimensional notion of Eliashberg-Thurston. As a second application of our main theorem, we then give an example, in any ambient odd dimension, of a c-symplectic (and in fact strong symplectic) foliation that cannot be contact approximated, in either of these two senses. This relies on the property, of independent interest, that contact structures approximating (in these senses) a weakly c-symplectic confoliation are also weakly fillable. The proofs of all these statements rely on pseudo-holomorphic curve theory. Lastly, we describe several natural classes of examples of these types of contact approximations of c-symplectic confoliations.
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BibTeX
@misc{gironella2026some,
title = {{On some rigidity results for high-dimensional confoliations}},
author = {Fabio Gironella and Seungook Yu},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13927},
eprint = {2610.13927},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05797628v1},
}
RIS
TY - UNPB
TI - On some rigidity results for high-dimensional confoliations
AU - Fabio Gironella
AU - Seungook Yu
PY - 2026
DA - 2026/10/09
PB - HAL
DO - 10.48550/arxiv.2610.13927
UR - https://hal.science/hal-05797628v1
AB - The main result is an obstruction to the presence of contact regions for c-symplectic confoliations in any odd ambient dimension. As a first application, we prove a 5-dimensional analogue (under stronger assumptions) of a Reeb stability theorem for confoliations in dimension 3 due to Eliashberg and Thurston. Refining work of the first author with Cardona, we further give two new notions of contact approximations of c-symplectic confoliations in any odd ambient dimension generalizing the 3-dimensional notion of Eliashberg-Thurston. As a second application of our main theorem, we then give an example, in any ambient odd dimension, of a c-symplectic (and in fact strong symplectic) foliation that cannot be contact approximated, in either of these two senses. This relies on the property, of independent interest, that contact structures approximating (in these senses) a weakly c-symplectic confoliation are also weakly fillable. The proofs of all these statements rely on pseudo-holomorphic curve theory. Lastly, we describe several natural classes of examples of these types of contact approximations of c-symplectic confoliations.
ER -