Impossible configurations for geodesics on negatively-curved surfaces

2019/02/24 by Phillips, Anthony
#53C22 57M50 30F99 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1902.09027

Abstract

Hass and Scott's example of a 4-valent graph on the 3-punctured sphere that cannot be realized by geodesics in any metric of negative curvature is generalized to impossible configurations filling surfaces of genus n with k punctures for any n and k.

Related

• Configurations of curves and geodesics on surfaces
• Multiple curves on punctured orientable surfaces
• Obstructions for generalized graphmanifolds to be nonpositively curved
• Algorithm for filling curves on surfaces
• Veering branched surfaces, surgeries, and geodesic flows