AI 中文总结
研究四维球面上打结曲面的跨越实体构造，借助村杉和的四维类似物定义树状打结曲面概念，通过给出例子及应用于破碎曲面图，确定交叉点分辨率以产生跨越实体。
AI 中文摘要
我们研究了四维球面上打结曲面的各种跨越实体构造。特别地，考虑了村杉和的四维类似物，用它定义了树状打结曲面的概念。给出了各种例子及在破碎曲面图中的应用，比如确定这些图中交叉点的哪些分辨率能产生跨越实体。
英文摘要
We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define a notion of arborescent knotted surfaces. We give a variety of examples and applications to broken surface diagrams, such as deciding which resolutions of the crossings in these diagrams yield spanning solids.
Comments60 pages+references, 63 figures
