14 research outputs found

    Five-Torsion in the Homology of the Matching Complex on 14 Vertices

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    J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex M14M_{14} on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case n=14n=14 is exceptional; for all other nn, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of MnM_n when n13n \ge 13 and n14n \neq 14.Comment: 11 page

    Infinitely Many Hyperbolic 3-manifolds Which Contain No Reebless Foliation

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    We investigate group actions on simply-connected (second countable but not necessarily Hausdorff) 1-manifolds and describe an infinite family of closed hyperbolic 3-manifolds whose fundamental groups do not act nontrivially on such 1-manifolds. As a corollary we conclude that these 3-manifolds contain no Reebless foliation. In fact, these arguments extend to actions on oriented -order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken

    Non-Right-Orderable 3-Manifold Groups

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    Moving Faces to Other Places: Facet Derangements

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    Topology of Colors (Extended Abstract)

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    IL-10 gene therapy prevents TNBS-induced colitis

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    The transfer of genes encoding immunomodulatory proteins to the intestinal mucosa is a promising new approach to the treatment of Crohn's disease (CD). This study investigates the therapeutic efficacy of an adenoviral vector encoding IL-10 (AdvmuIL-10) in experimental colitis. BALB/c mice were treated with a single intravenous injection of AdvmuIL-10, empty cassette virus (Adv0) or PBS prior to the induction of trinitrobenzene sulphonic acid (TNBS) colitis. AdvmuIL-10 treatment prevented the severe loss of body weight associated with TNBS administration. In addition, AdvmuIL-10 therapy led to a significant reduction in both stool markers of inflammation (IL-1beta and TNFR-II) and acute phase response (serum amyloid protein). Finally, the histological scores of mice with TNBS colitis treated with AdvmuIL-10 were significantly lower than Adv0- or PBS-treated controls. The therapeutic efficacy of AdvmuIL-10 was associated with a decrease in the IFN-gamma and IL-6 levels detected in colonic homogenates from mice with TNBS colitis, whereas no effect was observed on cytokine release from stimulated systemic lymphocytes. Thus, AdvmuIL-10 is an effective therapy in the TNBS model of colitis. Gene therapy strategies using adenoviral vectors encoding IL-10 may prove to be a potent therapy for chronic inflammatory conditions such as C
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