The Tropical Manin–Mumford Conjecture

Abstract In analogy with the Manin–Mumford conjecture for algebraic curves, one may ask how a metric graph under Abel–Jacobi embedding intersects torsion points of its Jacobian. We show that number is finite graphs genus ${g\geq 2}$, which are biconnected and have edge lengths “sufficiently irrational” in precise sense. Under these assumptions, bounded by $3g-3$. Next, we study bounds on image higher-degree embeddings, send $d$-tuples to This motivates definition “independent girth” graph, sharp upper bound $d$ such property holds.