The effect of infecting curves on knot concordance

Bridget D. Franklin

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arXiv · 1103.0254

The effect of infecting curves on knot concordance

Bridget D. Franklin

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Abstract

Various obstructions to knot concordance have been found using Casson-Gordon invariants, higher-order Alexander polynomials, as well as von-Neumann rho-invariants. Examples have been produced using (iterated) doubling operations K=R(c,J), and considering these as parametrized by invariants of the base knot J and doubling operator R. In this paper, we introduce a new mew method to obstruct concordance. We show that infinitely many distinct concordance classes may be constructed by varying the infecting curve c in S^3-R. Distinct concordance classes are found even while fixing the base knot, the doubling operator, and the order of c in the Alexander module.

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Bridget D. Franklin. 2011-03-01. The effect of infecting curves on knot concordance. https://arxiv.org/abs/1103.0254

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