Contact domination
Symplectic Geometry
2025-02-20 v1 Differential Geometry
Abstract
In this note, we prove that every closed connected oriented odd-dimensional manifold admits a map of non-zero degree (i.e., a domination) from a tight contact manifold of the same dimension. This provides an odd-dimensional counterpart of a symplectic domination result due to Joel Fine and Dmitri Panov. We prove that the dominating contact manifold can be ensured to be Liouville-fillable, but not Weinstein-fillable in general. We discuss an application for contact divisors arising as zero sets of asymptotically contact-holomorphic sections.
Keywords
Cite
@article{arxiv.2502.13927,
title = {Contact domination},
author = {Sekh Kiran Ajij and Ritwik Chakraborty and Balarka Sen},
journal= {arXiv preprint arXiv:2502.13927},
year = {2025}
}
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15 pages