Аннотация:
Many interesting examples of embeddings are embeddings S^p x S^q -> R^m, i.e.
knotted tori . A classification of knotted tori is a natural next step (after
the link theory and the classification of embeddings of highly-connected
manifolds ) towards classification of embeddings of arbitrary manifolds.
Since the general Knotting Problem is very hard, it is very interesting to
solve it for the important
particular case of knotted tori. Recent classification results for
knotted tori give some insight or even precise information concerning
arbitrary manifolds and reveal new interesting relations to algebraic
topology.
A description of the set of smooth isotopy classes of smooth embeddings
S^p x S^q -> R^m was known only for p=0, m>q+2 or for 2m>3p+3q+3.
For m>2p+q+2 we introduce a group structure on this set and describe this
group up to an extension problem (in terms of homotopy groups of spheres and
Stiefel manifolds).
In the proof we use a recent exact sequence of M. Skopenkov.
www.mccme.ru/~skopenko
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