Topology of plane sections of periodic polyhedra with an application to the truncated octahedron.
A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of...
The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.