Search arXivSearch

arXiv · 2005.05134

On oriented planar trees with three leaves

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.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jack Morava. 2020-05-14. On oriented planar trees with three leaves. https://arxiv.org/abs/2005.05134

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Cut pairs and Morse splitting of finitely generated groups

Bowditch's theorem for hyperbolic groups establishes a fundamental correspondence between splittings over two-ended subgroups and the existence of local cut points in the Gromov boundary. While analogous results have been obtained for CAT(0) and relatively hyperbolic groups, no general theorem of this type exists for arbitrary finitely generated groups. The Morse boundary, introduced by Charney-Sultan and extended by Cordes, provides a quasi-isometry invariant boundary for any finitely generated group that naturally generalizes the Gromov boundary. In this paper, we prove that a splitting of a finitely generated group with connected Morse boundary over a two-ended Morse subgroup gives rise to a separating pair of points in the Morse boundary.

math.GT

Khovanov Homology in Connected Sums

Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting the 3-manifold along a separating sphere, we construct type D and type A structures that are invariants of tangles in the two halves following the work of Roberts. Gluing the type D and type A structures along the common boundary recovers the Khovanov homology of the link.

math.GT

Fox-Milnor condition for concordant knots in homology 3-spheres

This paper will show that the Alexander polynomial of a knot, which is of slice type in an oriented homology 3-sphere, obeys the Fox-Milnor polynomial condition. A relation between Alexander polynomial of concordant knots in an oriented homology 3-sphere is established.

math.GT