3,265 research outputs found

    A Generalized Axis Theorem for Cube Complexes

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    We consider a finitely generated virtually abelian group GG acting properly and without inversions on a CAT(0) cube complex XX. We prove that GG stabilizes a finite dimensional CAT(0) subcomplex Y⊆XY \subseteq X that is isometrically embedded in the combinatorial metric. Moreover, we show that YY is a product of finitely many quasilines. The result represents a higher dimensional generalization of Haglund's axis theorem.Comment: 14 pages Corrected proof of Corollary 1.4. Various other corrections made following referee report and comments made by thesis examiner. Appendix added giving a proof of a theorem by Gerasimo

    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

    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

    Charge structure in volcanic plumes: a comparison of plume properties predicted by an integral plume model to observations of volcanic lightning during the 2010 eruption of Eyjafjallajökull, Iceland

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    Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption of Eyjafjallajökull allow the trajectory and growth of the volcanic plume to be determined. The lightning observations are compared with predictions of an integral model of volcanic plumes that includes descriptions of the interaction with wind and the effects of moisture. We show that the trajectory predicted by the integral model closely matches the observational data and the model well describes the growth of the plume downwind of the vent. Analysis of the lightning signals reveals information on the dominant charge structure within the volcanic plume. During the Eyjafjallajökull eruption both monopole and dipole charge structures were observed in the plume. By using the integral plume model, we propose the varying charge structure is connected to the availability of condensed water and low temperatures at high altitudes in the plume, suggesting ice formation may have contributed to the generation of a dipole charge structure via thunderstorm-style ice-based charging mechanisms, though overall this charging mechanism is believed to have had only a weak influence on the production of lightning

    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

    Unsteady turbulent buoyant plumes

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    We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the conservation of mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly described by shape factors in the integral equations; the commonly-assumed top-hat profiles lead to shape factors equal to unity. The resultant model is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity, differs from unity. The solutions of the model when source conditions are maintained at constant values retain the form of the well-established steady plume solutions. We demonstrate that the inclusion of a momentum shape factor that differs from unity leads to a well-posed integral model. Therefore, our model does not exhibit the mathematical pathologies that appear in previously proposed unsteady integral models of turbulent plumes. A stability threshold for the value of the shape factor is identified, resulting in a range of its values where the amplitude of small perturbations to the steady solutions decay with distance from the source. The hyperbolic character of the system allows the formation of discontinuities in the fields describing the plume properties during the unsteady evolution. We compute numerical solutions to illustrate the transient development following an abrupt change in the source conditions. The adjustment to the new source conditions occurs through the propagation of a pulse of fluid through the plume. The dynamics of this pulse are described by a similarity solution and, by constructing this new similarity solution, we identify three regimes in which the evolution of the transient pulse following adjustment of the source qualitatively differ.Comment: 41 pages, 16 figures, under consideration for publication in Journal of Fluid Mechanic

    Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

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    The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures ΩΨ0\Omega_{\Psi_0} on the moduli space, parametrised by Ψ0\Psi_0, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles PΨ0{\mathcal P}_{\Psi_0} on the moduli space whose curvature is proportional to the symplectic forms ΩΨ0\Omega_{\Psi_0}.Comment: 8 page
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