The projections of n-knots which are not the projection of any unknotted knot

Details The projections of n-knots which are not the projection of any unknotted knot The projections of n-knots which are not the projection of any unknotted knot

2000-03-15

arxiv.org/abs/math/0003088v1

Mathematics

Geometric Topology

12 pages, no figure

Scientific paper

Let n be any integer greater than two. We prove that there exists a projection P having the following properties. (1) P is not the projection of any unknotted knot. (2) The singular point set of P consists of double points. (3) P is the projection of an n-knot which is diffeomorphic to the standard sphere. We prove there exists an immersed n-sphere (in R^{n+1}\times{0}) which is not the projection of any n-knot (n>2). Note that the second theorem is different from the first one.

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