The rational classification of links of codimension > 2

Diarmuid John Crowley, Steven C. Ferry, Mikhail Skopenkov

Research output: Contribution to journalArticle

2 Citations (Scopus)
3 Downloads (Pure)

Abstract

Let m and be positive integers. The set of links of codimension , , is the set of smooth isotopy classes of smooth embeddings . Haefliger showed that is a finitely generated abelian group with respect to embedded connected summation and computed its rank in the case of knots, i.e. . For and for restrictions on the rank of this group can be computed using results of Haefliger or Nezhinsky. Our main result determines the rank of the group in general. In particular we determine precisely when 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.
Original languageEnglish
Pages (from-to)239-269
Number of pages31
JournalForum Mathematicum
Volume26
Issue number1
DOIs
Publication statusPublished - Nov 2011

Fingerprint

Algebra
Codimension
Isotopy
Exact Sequence
Finitely Generated Group
Summation
Knot
Abelian group
Lie Algebra
Restriction
Integer
Class

Keywords

  • smooth manifold
  • embedding
  • isotopy
  • link
  • homotopy group
  • lie algebra

Cite this

Crowley, D. J., Ferry, S. C., & Skopenkov, M. (2011). The rational classification of links of codimension > 2. Forum Mathematicum, 26(1), 239-269. https://doi.org/10.1515/form.2011.158

The rational classification of links of codimension > 2. / Crowley, Diarmuid John; Ferry, Steven C.; Skopenkov, Mikhail.

In: Forum Mathematicum, Vol. 26, No. 1, 11.2011, p. 239-269.

Research output: Contribution to journalArticle

Crowley, DJ, Ferry, SC & Skopenkov, M 2011, 'The rational classification of links of codimension > 2', Forum Mathematicum, vol. 26, no. 1, pp. 239-269. https://doi.org/10.1515/form.2011.158
Crowley, Diarmuid John ; Ferry, Steven C. ; Skopenkov, Mikhail. / The rational classification of links of codimension > 2. In: Forum Mathematicum. 2011 ; Vol. 26, No. 1. pp. 239-269.
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