Higher-order analogues of the slice genus of a knot

Peter D. Horn

doi:10.1093/imrn/rnq115

Higher-order analogues of the slice genus of a knot

Peter D. Horn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1091-1106
Number of pages	16
Journal	International Mathematics Research Notices
Volume	2011
Issue number	5
DOIs	https://doi.org/10.1093/imrn/rnq115
State	Published - 2011

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnq115

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Higher-order analogues of the slice genus of a knot

Abstract

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