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. © 2004 Elsevier Ltd. All rights reserved.
Takase, M. (2004). A geometric formula for Haefliger knots. Topology, 43(6), 1425–1447. https://doi.org/10.1016/j.top.2004.03.001