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The rational classification of links of codimension > 2
-
Diarmuid Crowley
,
Steven C. Ferry
Published/Copyright:
November 4, 2011
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.
Received: 2011-07-08
Revised: 2011-09-30
Published Online: 2011-11-04
Published in Print: 2014-01-01
© 2014 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Pseudovarieties generated by Brauer type monoids
- On some arithmetic properties of Siegel functions (II)
- Perfect vector alignment of the vorticity and the vortex stretching is one forever
- Frobenius groups of automorphisms and their fixed points
- Schubert calculus and the Hopf algebra structures of exceptional Lie groups
- The sovability of norm, bilinear and quadratic equations over finite fields via spectra of graphs
- Periodicity in the stable representation theory of crystallographic groups
- Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
- The rational classification of links of codimension > 2
- On the classifying space for proper actions of groups with cyclic torsion
- Turán determinants of Bessel functions
