902 citations
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29 papers · 1 filter
Hierarchically hyperbolic spaces I: curve complexes for cubical groups
Jason Behrstock, Mark F. Hagen, Alessandro Sisto
In the context of CAT(0) cubical groups, we develop an analogue of the theory of curve complexes and subsurface projections. The role of the subsurfaces is played by a collection o…
Efficient geodesics and an effective algorithm for distance in the complex of curves
Joan Birman, Dan Margalit, William Menasco
We give an algorithm for determining the distance between two vertices of the complex of curves. While there already exist such algorithms, for example by Leasure, Shackleton, and…
Intercusp geodesics and the invariant trace field of hyperbolic 3-manifolds
Walter Neumann, Anastasiia Tsvietkova
Given a cusped hyperbolic 3-manifold with finite volume, we define two types of complex parameters which capture geometric information about the preimages of geodesic arcs travelin…
A tour of bordered Floer theory
Robert Lipshitz, Peter S. Ozsvath, Dylan P. Thurston
Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented…
Volume bounds for generalized twisted torus links
Abhijit Champanerkar, David Futer, Ilya Kofman +2
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knot…
Quasi-isometric classification of non-geometric 3-manifold groups
Jason Behrstock, Walter D Neumann
We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric component…