Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On boundary-link cobordism

Washington Mioa1

a1 Institute de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, Rio de Janeiro – R.J. – 22.460, Brazil

An n-dimensional m-component link is an oriented smooth submanifold Σn of Sn+2, where S0305004100066615_inline1 is the ordered disjoint union of m submanifolds of Sn+2, each homeomorphic to Sn. Σ is a boundary link if there is an oriented smooth submanifold Vn+1 of Sn+1, S0305004100066615_inline2 the disjoint union of the submanifolds S0305004100066615_inline3, such that ∂Vi = Σi (i = 1,…, m). A pair (Σ, V), where Σ is a boundary link and V as above, with each Vi connected (i = 1,…, m), is called an n-dimensional special Seifert pair. In this paper, we define a notion of cobordism of special Seifert pairs and give an algebraic description of the set (group) of cobordism classes.

(Received May 13 1986)