Higher-order analogues of the slice genus of a knot

Peter D. Horn

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Pages (from-to)1091-1106
Number of pages16
JournalInternational Mathematics Research Notices
Issue number5
StatePublished - 2011

ASJC Scopus subject areas

  • General Mathematics


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