The tropical Poincaré-Hopf theorem
| Autor: | Johannes Rau |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Algebraic Geometry
Mathematics::Combinatorics Computational Theory and Mathematics FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Combinatorics (math.CO) 14T20 05B35 52B40 55M20 Algebraic Geometry (math.AG) Physics::Atmospheric and Oceanic Physics Theoretical Computer Science |
| DOI: | 10.48550/arxiv.2007.11642 |
| Popis: | We express the beta invariant of a loopless matroid as tropical self-intersection number of the diagonal of its matroid fan (a "local" Poincar\'e-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 Poincar\'e-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. Comment: 31 pages, 3 figures; several improvements and corrections in the new version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|