Minimal contact triangulations of 3-manifolds

Basudeb Datta; Dheeraj Kulkarni

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arXiv · 1608.03823

Minimal contact triangulations of 3-manifolds

Basudeb Datta·Dheeraj Kulkarni

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Abstract

In this paper, we explore minimal contact triangulations on contact 3-manifolds. We give many explicit examples of contact triangulations that are close to minimal ones. The main results of this article say that on any closed oriented 3-manifold the number of vertices for minimal contact triangulations for overtwisted contact structures grows at most linearly with respect to the relative $d^3$ invariant. We conjecture that this bound is optimal. We also discuss, in great details, contact triangulations for a certain family of overtwisted contact structures on 3-torus.

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Basudeb Datta, Dheeraj Kulkarni. 2016-08-12. Minimal contact triangulations of 3-manifolds. https://arxiv.org/abs/1608.03823

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