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The ray graph is a Gromov hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray graph is homeomorphic to a quotient of a subset of the circle. This version contains some updates and corrections.
We show that in large enough rank, the Gromov boundary of the free factor complex is path connected and locally path connected.
Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of such curves a
We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.
We show that every knot is one crossing change away from a knot of arbitrarily high bridge number and arbitrarily high bridge distance.
Let n>2 and let M be an orientable complete finite volume hyperbolic n-manifold with (possibly empty) geodesic boundary having Riemannian volume vol(M) and simplicial volume ||M||. A celebrated result by Gromov and Thurston states that if M has empty