论文标题
在4D凸多图形上计算REEB动力学
Computing Reeb dynamics on 4d convex polytopes
论文作者
论文摘要
我们研究了四维凸层的边界上的组合芯片流。我们建立了多层的“组合芯片轨道”与普通的Reeb轨道之间的对应关系，以平滑多层，尊重动作和Conley-Zehnder索引。然后，人们可以使用计算机找到所有组合的Reeb轨道，直到给定的动作和Conley-Zhhnder索引。我们提供了测试Viterbo的猜想和相关猜想的实验结果。特别是，我们发现了一些收缩比$ 1 $的多台面的新示例。
We study the combinatorial Reeb flow on the boundary of a four-dimensional convex polytope. We establish a correspondence between "combinatorial Reeb orbits" for a polytope, and ordinary Reeb orbits for a smoothing of the polytope, respecting action and Conley-Zehnder index. One can then use a computer to find all combinatorial Reeb orbits up to a given action and Conley-Zehnder index. We present some results of experiments testing Viterbo's conjecture and related conjectures. In particular, we have found some new examples of polytopes with systolic ratio $1$.
