A knot bounding a grope of class n is n/2-trivial

Details A knot bounding a grope of class n is n/2-trivial A knot bounding a grope of class n is n/2-trivial

1999-07-23

arxiv.org/abs/math/9907158v2

Mathematics

Geometric Topology

32 pages, 25 figures, additional reference material added

Scientific paper

In this article it is proven that if a knot, K, bounds an imbedded grope of class n, then the knot is n/2-trivial in the sense of Gusarov and Stanford. That is, all type n/2 invariants vanish on K. We also give a simple way to construct all knots bounding a grope of a given class. It is further shown that this result is optimal in the sense that for any n there exist gropes which are not n/2+1- trivial.

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