Here we illustrate how Jones’ polynomials are derived from the kinetic helicity of vortical flows, and how they can be used to measure the topological complexity of fluid knots by numerical values. Relying on this new findings, we show how to use our adapted Jones polynomial in a new framework by introducing a knot polynomial space whose discrete points are the adapted Jones polynomials of fluid knots, interpreting the topological simplification associated with the natural decay of reconnecting fluid knots as geodesic flows on this space.

中文翻译：

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流体结琼斯多项式的新框架

在这里，我们说明了琼斯多项式是如何从涡流的动力学螺旋性导出的，以及如何使用它们通过数值来测量流体结的拓扑复杂性。依靠这一新发现，我们展示了如何在新框架中使用我们的适应琼斯多项式，通过引入一个结多项式空间，其离散点是流体结的适应琼斯多项式，解释与重新连接流体结的自然衰减相关的拓扑简化当测地线在这个空间上流动时。