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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 101, Issue 2
  • March 1987, pp. 259-266

On boundary-link cobordism

  • Washington Mio (a1)
  • DOI:
  • Published online: 24 October 2008

An n-dimensional m-component link is an oriented smooth submanifold Σn of Sn+2, where 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, the disjoint union of the submanifolds , 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.

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[1]S. E. Cappell and J. L. Shaneson . Link cobordism, Comment. Math. Helv. 55 (1980), 2049.

[2]S. E. Cappell and J. L. Shaneson . The codimension two placement problem and homology equivalent manifolds. Ann. of Math. 99 (1974), 277348.

[3]M. Gutierrez . Boundary links and an unlinking theorem. Trans. Amer. Math. Soc. 171 (1972), 491499.

[4]M. Hirsch . Embeddings and compressions of polyhedra and smooth manifolds. Topology 4 (1966), 361369.

[7]J. Levine . Knot cobordism groups in codimension two. Comment. Math. Helv. 44 (1968), 229244.

[8]J. Levine . Invariants of knot cobordism. Inventiones Math. 8 (1969), 98110.

[9]J. Levine . Polynomial invariants of knots of codimension two. Ann. of Math. 84 (1966), 537554.

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Mathematical Proceedings of the Cambridge Philosophical Society
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