134 research outputs found

    Classifying Finite Dimensional Cubulations of Tubular Groups

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    A tubular group is a group that acts on a tree with Z2\mathbb{Z}^2 vertex stabilizers and Z\mathbb{Z} edge stabilizers. This paper develops further a criterion of Wise and determines when a tubular group acts freely on a finite dimensional CAT(0) cube complex. As a consequence we offer a unified explanation of the failure of separability by revisiting the non-separable 3-manifold group of Burns, Karrass and Solitar and relating it to the work of Rubinstein and Wang. We also prove that if an immersed wall yields an infinite dimensional cubulation then the corresponding subgroup is quadratically distorted.Comment: 24 pages, 11 figures. Minor corrections and clarifications. Some figures are redrawn. The proof of Theorem 6.1 is rewritten for clarity and to correct error

    A Cubical Flat Torus Theorem and the Bounded Packing Property

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    We prove the bounded packing property for any abelian subgroup of a group acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of the proof is a cubical flat torus theorem. This ingredient is also used to show that central HNN extensions of maximal free-abelian subgroups of compact special groups are virtually special, and to produce various examples of groups that are not cocompactly cubulated.Comment: 14 pages, 2 figures, submitted May 2015 Minor corrections and swapped sections 2 and 3 Corrected an unfortunate typo in Theorem 2.1 - the hypothesis that the cube complex be finite dimensional has now been adde

    Hyperbolic groups that are not commensurably coHopfian

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    Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In particular, we show that the fundamental group of every simple surface amalgam is not commensurably coHopfian.Comment: v3: 14 pages, 4 figures; minor changes. To appear in International Mathematics Research Notice

    The application of deep eutectic solvent ionic liquids for environmentally-friendly dissolution and recovery of precious metals

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    publisher: Elsevier articletitle: The application of deep eutectic solvent ionic liquids for environmentally-friendly dissolution and recovery of precious metals journaltitle: Minerals Engineering articlelink: http://dx.doi.org/10.1016/j.mineng.2015.09.026 content_type: article copyright: Copyright © 2015 The Authors. Published by Elsevier Ltd.© 2015 Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)