标题： 扭结缺陷在有界域中的同伦分类 显示英文标题

标题： Homotopy classification of knotted defects in bounded domains

摘要： Nozaki等人通过考虑从空间图补集到序参量空间的连续映射，并在某种等价关系下，给出了三维空间中结缺陷的同伦分类。 我们通过围绕经向环的单色群，将全局缺陷描述为边由序参量空间基本群元素着色的平面图，从而扩展了他们的结果，给出了手柄体中有序介质的分类方案，其中缺陷允许到达边界。 我们在正八面体框架场和双轴向列液晶中展示了这种分类的例子。 显示英文摘要

摘要： Nozaki et.~al.\ gave a homotopy classification of the knotted defects of ordered media in three-dimensional space by considering continuous maps from complements of spatial graphs to the order parameter space modulo a certain equivalence relation. We extend their result by giving a classification scheme for ordered media in handlebodies, where defects are allowed to reach the boundary. Through monodromies around meridional loops, global defects are described in terms of planar diagrams whose edges are colored by elements of the fundamental group of the order parameter space. We exhibit examples of this classification in octahedral frame fields and biaxial nematic liquid crystals.