The rational classification of links of codimension > 2

Diarmuid J. Crowley, Steven C. Ferry, Mikhail Skopenkov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Let m and p1,.,pr < m - 2 be positive integers. The set of links of codimension > 2, Em(∐k=1 rSPk), is the set of smooth isotopy classes of smooth embeddings ∐k=1 rSPk → Sm. Haefliger showed that Em(∐k=1 rSPk) is a finitely generated abelian group with respect to embedded connected summation and computed its rank in the case of knots, i.e. r = 1. For r > 1 and for restrictions on p1,.,pr the rank of this group can be computed using results of Haefliger or Nezhinsky. Our main result determines the rank of the group Em(∐k=1 rSPk) in general. In particular we determine precisely when Em(∐k=1 rSPk) is finite. We also accomplish these tasks for framed links. Our proofs are based on the Haefliger exact sequence for groups of links and the theory of Lie algebras. © de Gruyter 2014.
Original languageEnglish (US)
Pages (from-to)239-269
Number of pages31
JournalForum Mathematicum
Volume26
Issue number1
DOIs
StatePublished - Jan 1 2014

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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