Higher-order Analogues of the Slice Genus of a Knot

Peter D. Horn

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arXiv · 0807.0434

Higher-order Analogues of the Slice Genus of a Knot

Peter D. Horn

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Abstract

For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higher-order genera in terms of certain von Neumann $ρ$-invariants, which we call higher-order signatures. The higher-order genera offer a refinement of the Grope filtration of the knot concordance group.

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Peter D. Horn. 2010-06-02. Higher-order Analogues of the Slice Genus of a Knot. https://arxiv.org/abs/0807.0434

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