Self-Linking Invariants of Embeddings in the Metastable Range.
Simplexwise linear and piecewise linear near self-homeomorphisms of surfaces
Special positions for surfaces bounded by closed braids.
Steenrod operations in subanalytic homology
Submanifolds of codimension two and homology equivalent manifolds
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 -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
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...