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arXiv · 2502.13927

Contact domination

Sekh Kiran Ajij·Ritwik Chakraborty·Balarka Sen
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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.

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Sekh Kiran Ajij, Ritwik Chakraborty, Balarka Sen. 2025-02-19. Contact domination. https://arxiv.org/abs/2502.13927

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