论文标题
热带Poincaré-Hopf定理
The tropical Poincaré-Hopf theorem
论文作者
论文摘要
我们表达了无环形矩阵的beta不变，是其矩阵风扇的对角线的热带自我交流数（“局部”poincaré-hopf定理）。这提供了另一个例子，即通过在热带化的几何结构方面表达其不变性来揭示其“几何”。我们还证明了全球庞加尔 - 霍普定理，并通过证明两种特殊的热带曲线和热带托里的特殊情况来启动更一般的热带lefschetz-hopf痕量痕量公式。
We express the beta invariant of a loopless matroid as tropical self-intersection number of the diagonal of its matroid fan (a "local" Poincaré-Hopf theorem). This provides another example of uncovering the "geometry" of matroids by expressing their invariants in terms of tropicalised geometric constructions. We also prove a global Poincaré-Hopf theorem and initiate the study of a more general tropical Lefschetz-Hopf trace formula by proving the two special cases of tropical curves and tropical tori.
