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Link cobordism.

Sylvain E. Cappell, Julius L. Shaneson (1980)

Commentarii mathematici Helvetici

Link homotopy invariants of graphs in R3.

Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we define a link homotopy invariant of spatial graphs based on the second degree coefficient of the Conway polynomial of a knot.

Properly homotopic nontrivial planes are isotopic

Bobby Winters (1995)

Fundamenta Mathematicae

It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to 3 are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.

Submanifolds of codimension two and homology equivalent manifolds

Sylvain E. Cappell, Julius L. Shaneson (1973)

Annales de l'institut Fourier

In this paper new methods of studying codimension two embeddings of manifolds are outlined. Results are stated on geometric periodicity of knot cobordism. The group of local knots of a manifold in a 2-plane bundle is introduced and computed, and applied to C o -close embeddings. General codimension two splitting theorems are discussed, with applications to equivariant knots and knot cobordism. A general existence theorem for P.L. (non-locally flat) embeddings is also given.The methods involve some...

Surfaces in 3-space that do not lift to embeddings in 4-space

J. Carter, Masahico Saito (1998)

Banach Center Publications

A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic is immersed...

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