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SEIFERT FIBERED KNOT MANIFOLDS

School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia

and

Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

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https://doi.org/10.1142/S021821651350082XCited by:1 (Source: Crossref)

Abstract

We consider the question of when is the closed manifold obtained by elementary surgery on an n-knot Seifert fibered over a 2-orbifold. The possible bases are strongly constrained by the fact that knot groups have weight 1. We present a new family of 2-knots with solvable groups, overlooked in earlier work. The knots in this new family are neither invertible nor amphicheiral, and the weight orbits for the knot groups are parametrized by ℤ. There are no known examples in higher dimensions.

Keywords:

AMSC: 57M25, 57Q45

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