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Forum Mathematicum

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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 26, Issue 1 (Jan 2014)

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The rational classification of links of codimension > 2

Diarmuid Crowley
  • Hausdorff Research Institute for Mathematics, Poppelsdorfer Allee 82, 53115 Bonn, Germany
  • Email:
/ Steven C. Ferry
  • Department of Mathematics, Rutgers University, Hill Center, Busch Campus, Piscataway, NJ 08854-8019, USA
  • Email:
/ Mikhail Skopenkov
  • King Abdullah University of Science and Technology, P. O. Box 2187, 4700 Thuwal, 23955-6900, Kingdom of Saudi Arabia, and Institute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny per. 19, bld. 1, Moscow, 127994, Russian Federation
  • Email:
Published Online: 2011-11-04 | DOI: https://doi.org/10.1515/form.2011.158

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.

Keywords: Smooth manifold; embedding; isotopy; link; homotopy group; Lie algebra

About the article

Received: 2011-07-08

Revised: 2011-09-30

Published Online: 2011-11-04

Published in Print: 2014-01-01



Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.158. Export Citation

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Mikhail Skopenkov
International Journal of Mathematics, 2015, Volume 26, Number 07, Page 1550051

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