The tropical Poincare-Hopf theorem

被引：1

作者：

Rau, Johannes ^{[1
]}

机构：

[1] Univ Los Andes, Dept Matemat, KR 1 18 A 10, BL H, Bogota, Colombia

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2023年 / 196卷

关键词：

Tropical geometry; Matroid theory; Tropical homology; Tropical intersection theory; Poincare-Hopf theorem;

D O I：

10.1016/j.jcta.2023.105733

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We express the beta invariant of a loopless matroid as tropical self-intersection number of the diagonal of its matroid fan (a "local" Poincare-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 Poincare-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.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

引用

页数：28

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