环面拓扑上的自对偶码和切除结构

It's known that many kinds of mathematics meet in Toric Topology. Here Two topics are considered.. One is about self-dual codes. Self-dual codes are very important in coding theory. We have found a natural connection between self-dual codes and some mod 2 quasi-toric manifolds. We want to consider the further question about them, especial the relationship between simple convex polytopes and self-dual codes.. The other is the open book decomposition and contact structure on some mod 2 quasi-toric manifolds. It's very interested to consider the sturcture invariant under the toric action. We hope to find some result in form of combinatoric of simple polytopes. . Since the two topic are relized on some special toric manifolds, we also want to consider the relation between them.

环面拓扑是一个交叉性很强的领域。本项目立足环面拓扑，研究两个主题。. 一是线性自对偶码。自对偶码是编码理论中重要的研究对象。我们发现一类模2拟环面流形上，有自然的自对偶码。我们将详细探讨自对偶码与环面拓扑之间的关联，特别是单凸多面体的组合结构与自对偶码之间的关系。. 二是模模2拟环面流形上开书结构和切触结构。我们对于在环面群作用下保持不变的开书分解和切触结构非常感兴趣。由于环面拓扑与多面体的组合结构之间存在密切的联系，我们希望给出它们的组合对应。开书结构与切触结构之间关系密切，我们也将建立开书结构的组合对应。. 最后，自对偶码与开书结构和切触结构都建立在同一类模2拟环面流形上，我们希望能探讨它们之间的关联。