BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 39 39-45 2007年2月 [査読有り]
We give a formula for the bordism class of an immersion of an oriented 3-manifold in 4-space. It expresses the class in terms of the topology of a null-cobordism of the 3-manifold and certain singularities (the number of umbilic points) of a gener...
ALGEBRAIC AND GEOMETRIC TOPOLOGY 7 359-377 2007年 [査読有り]
Using spinning we analyze in a geometric way Haefliger's smoothlyknotted (4k-1)-spheres in the 6k-sphere. Consider the 2-torus standardly embedded in the 3-sphere, which is further standardly embedded in the 6-sphere. At each point of the 2-torus ...
INTERNATIONAL JOURNAL OF MATHEMATICS 17(8) 869-885 2006年9月 [査読有り]
For smooth embeddings of an integral homology 3-sphere in the 6-sphere, we define an integer invariant in terms of their Seifert surfaces. Our invariant gives a bijection between the set of smooth isotopy classes of such embeddings and the integer...
Haefliger has shown that a smooth embedding of the (4k-1)-sphere in the 6k-sphere can be knotted in the smooth sense. In this paper, we give a formula with which we can detect the isotopy class of such a Haefliger knot. The formula is expressed in...
We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric formulae for t...
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