论文标题
广义的棋盘综合体和离散的摩尔斯理论
Generalized chessboard complexes and discrete Morse theory
论文作者
论文摘要
棋盘复合体及其作为对象和离散的摩尔斯理论作为工具的概括作为统一的主题，将几何，拓扑，代数和组合学领域的不同领域连接起来。 Edmonds和Fulkerson瓶颈（Minmax）定理被证明和解释，是关于相关的Simplicial Complect $ K $在Bier Sphere上离散摩尔斯的关键点的结果。我们通过证明具有多重性的棋盘配合物的连通性结果来说明在广义棋盘复合体上使用“标准离散摩尔斯函数”。应用程序包括新的tverberg-van kampen-flores类型的结果，用于$ j $ - 单纯的分区。
Chessboard complexes and their generalizations, as objects, and Discrete Morse theory, as a tool, are presented as a unifying theme linking different areas of geometry, topology, algebra and combinatorics. Edmonds and Fulkerson bottleneck (minmax) theorem is proved and interpreted as a result about a critical point of a discrete Morse function on the Bier sphere of an associated simplicial complex $K$. We illustrate the use of "standard discrete Morse functions" on generalized chessboard complexes by proving a connectivity result for chessboard complexes with multiplicities. Applications include new Tverberg-Van Kampen-Flores type results for $j$-wise disjoint partitions of a simplex.
