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1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same pathsExpand
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Mixed 3-manifolds are virtually special
LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that π1M is virtually special.
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Arcs intersecting at most once
We prove that on a punctured oriented surface with Euler characteristic $${\chi < 0}$$χ<0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersectingExpand
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Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs
We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same pathsExpand
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Separability of embedded surfaces in 3-manifolds
We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.
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Cocompactly cubulated graph manifolds
Let M be a graph manifold. We show that π1M is the fundamental group of a compact nonpositively curved cube complex if and only if M is chargeless. We also prove that in that case π1M is virtuallyExpand
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Twist-rigid Coxeter groups
We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basicExpand
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Boundaries of systolic groups
For all systolic groups we construct boundaries which are EZ--structures. This implies the Novikov conjecture for torsion--free systolic groups. The boundary is constructed via a system ofExpand
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A note on acylindrical hyperbolicity of Mapping Class Groups
The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs areExpand
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Cocompactly cubulated 2-dimensional Artin groups
We give a necessary and sufficient condition for a 2-dimensional or a three-generator Artin group $A$ to be (virtually) cocompactly cubulated, in terms of the defining graph of $A$.
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