5,072 research outputs found

    Surgery on SL~×En\widetilde{\Bbb{SL}}\times\Bbb{E}^n-manifolds

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    We show that although closed SL~×En\widetilde{\Bbb{SL}}\times\Bbb{E}^n-manifolds do not admit metrics of nonpositive sectional curvature, the arguments of Farrell and Jones can be extended to show that such manifolds are topologically rigid, if n≥2n\geq2.Comment: 7 pages, AMS-LaTeX file, To appear in the Canadian Mathematical Bulletin

    Seifert fibred knot manifolds

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    We consider the question of when is the closed manifold obtained by elementary surgery on an nn-knot Seifert fibred over a 2-orbifold. After some observations on the classical case, we concentrate on the cases n=2 and 3. We have found a new family of 2-knots with torsion-free, solvable group, overlooked in earlier work. We know of no higher dimensional examples.Comment: New co-author, stronger restrictions on possible Seifert bases. Final section on 3-knots reduced to a paragraph, as a lemma was misused in the original version. Version 3; minor improvements to first paragraph and notatio
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