Geometry in the interface between high- and low-dimensional Topology

点击翻译按钮获取中文摘要

We show that any 3-sphere embedded in the 6-sphere can be obtained by performing the operation called spinning about submanifold, introduced by Dennis Roseman in 1989. Also, we analyze the possible values of a certain Hopf invariant, which is defined for such a 3-sphere embedded in the 6-sphere. And also, for a given immersion of the 3-sphere into the 4-space, we give a formula with which we can read off its bordism class from some geometric information on singularities of its extension by a generic map.