ABSTRACT

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modify transport properties in their vicinity as if the geometry was non-Euclidean. We present a state-of-the-art of differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics and conclude with a review on defect engineering for transport phenomena.

中文翻译：

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拓扑缺陷的几何理论：方法论的发展和新趋势

摘要

液晶通常支持称为拓扑缺陷的指向矢场的取向奇点。后者修改它们附近的传输属性，就好像几何是非欧几里德的一样。我们展示了向列液晶微分几何的最新技术，特别强调了线性缺陷。然后，我们讨论了与宇宙学和高能物理学的意想不到但深刻的联系，并以对传输现象的缺陷工程的回顾作为总结。