Link cobordism.
Link homotopy invariants of graphs in R3.
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.
Obstructions to Embedding and Isotopy in the Metastable Range.
On Quadratic Forms in 3-Manifolds.
On Representing Homology Classes of 4-Manifolds.
On surface braids of index four with at most two crossings
Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.
On the homotopy embeddability of complexes in Euclidean space. I. The weak thickening theorem.
On the homotopy invariance of configuration spaces.
On the planarity of 2-complexes
On the Space of the Linear Homeomorphisms of a Polyhedral TV-Cell with Two Interior Vertices*.
Polyedrische 2-Mannigfaltigkeiten mit wenigen nicht-konvexen Ecken.
Projections of knots
Properly homotopic nontrivial planes are isotopic
It is proved that two planes that are properly homotopic in a noncompact, orientable, irreducible 3-manifold that is not homeomorphic to are isotopic. The end-reduction techniques of E. M. Brown and C. D. Feustal and M. G. Brin and T. L. Thickstun are used.
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...
The combinatorial formula of Gabrielov, Gelfand and Losik for the first Pontrjagin class