半边图在穿孔曲面中的嵌入
Embedding Half-Edge Graphs in Punctured Surfaces
摘要：
众所周知，嵌入曲面的细胞图等价于带状图。在这项工作中，我们将这一说法推广到更广泛的类图和曲面。边图是抽象图的推广，在物理学中的量子场论中很有用.另一方面，具有半边的带状图推广了带状图，并出现在源自矩阵模型的不同类型的域论中。然后，我们给出了一个意义上的嵌入半边图穿孔表面和确定（最小/最大）这些嵌入和半边缘带状图之间的等价条件。在给定嵌入的一些假设条件下，还证明了嵌入半边图的几何对偶。
英文摘要：
It is known that graphs cellularly embedded into surfaces are equivalent to ribbon graphs. In this work, we generalize this statement to broader classes of graphs and surfaces. Half-edge graphs extend abstract graphs and are useful in quantum field theory in physics. On the other hand, ribbon graphs with half-edges generalize ribbon graphs and appear in a different type of field theory emanating from matrix models. We then give a sense of embeddings of half-edge graphs in punctured surfaces and determine (minimal/maximal) conditions for an equivalence between these embeddings and half-edge ribbon graphs. Given some assumptions on the embedding, the geometric dual of a cellularly embedded half-edge graph is also identified.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
