A geometric formula for Haefliger knots |
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Authors: | Masamichi Takase |
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Institution: | Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, 79-1 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501 Japan |
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Abstract: | 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 terms of the geometric characteristics of an extension, analogous to a Seifert surface, of the given embedding. In particular, the Hopf invariant associated to the extension plays a crucial role. This leads us to a new characterisation of Haefliger knots. |
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Keywords: | Haefliger knot Geometric formula Differentiable isotopy Hopf invariant Sz?cs&rsquo linking |
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