2019/06/06 by Kudlinska, Monika
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1906.02577
Let Σ be a compact, orientable surface of negative Euler characteristic, and let h be a complete hyperbolic metric on Σ. A geodesic curve γ in Σ is filling, if it cuts the surface into topological disks and annuli. We propose an efficient algorithm for deciding whether a geodesic curve, represented as a word in some generators of π1(Σ), is filling. In the process, we find an explicit bound for the combinatorial length of a curve given by its Dehn-Thurston coordinate, in terms of the hyperbolic length. This gives us an efficient method for producing a collection which is guaranteed to contain all words corresponding to simple geodesics of bounded hyperbolic length.