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arXiv · 2408.00522

Relative Helicity and Tiling Twist

Boris Khesin·Nicolau C. Saldanha
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Abstract

We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These invariants allow one to classify the tilings with respect to certain elementary moves, flips and trits. In this paper we present a construction associating a divergence-free vector field $ξ_t$ to any domino tiling $t$, such that the flux of the tiling $t$ can be interpreted as the (relative) rotation class of the field $ξ_t$, while the twist of $t$ is proved to be the relative helicity of the field $ξ_t$.

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Boris Khesin, Nicolau C. Saldanha. 2025-03-13. Relative Helicity and Tiling Twist. https://arxiv.org/abs/2408.00522

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