Differential 3knots in 5space with and without self intersections
Abstract
Regular homotopy classes of immersions of a 3sphere in 5space constitute an infinite cyclic group. The classes containing embeddings form a subgroup of index 24. The obstruction for a generic immersion to be regularly homotopic to an embedding is described in terms of geometric invariants of its self intersection. Geometric properties of self intersections are used to construct two invariants J and St of generic immersions which are analogous to Arnold's invariants of plane curves. We prove that J and St are independent first order invariants and that any first order invariant is a linear combination of these. As byproducts, some invariants of immersions of 3spheres in 4space are obtained. Using them, we find restrictions on the topology of self intersections.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2000
 arXiv:
 arXiv:math/0002077
 Bibcode:
 2000math......2077E
 Keywords:

 Mathematics  Geometric Topology;
 57R42;
 57R45
 EPrint:
 35 pages, 7 figures, A newer version of this paper will appear in Topology