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

James Conant

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arXiv · math/9907158

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

James Conant

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Abstract

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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James Conant. 1999-07-30. A knot bounding a grope of class n is n/2-trivial. https://arxiv.org/abs/math/9907158

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