Short homotopically independent loops on surfaces
Short homotopically independent loops on surfaces
In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that for every closed Riemannian surface of genus $g \geq 2$ and area normalized to $g$, there are at least $\ceil{\log(2g)+1}$ homotopically independent …