On oriented planar trees with three leaves

preprint2020arXivOpen access

Abstract

This elementary note proposes candidates for interesting continuous piecewise-smooth `Riemannian' metrics on the moduli spaces of rooted geodesic trees embedded in the Poincaré disk. A related digression observes the existence of an apparently hitherto unrecognized abelian topological group structure on the real projective line.

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