Chapman's Classification of Shapes. A Proof Using Collapsing.
Characterization of knot complements in the n-sphere
Knot complements in the n-sphere are characterized. A connected open subset W of is homeomorphic with the complement of a locally flat (n-2)-sphere in , n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.
Combinatoire des simplexes sans singularités I. Le cas différentiable
On définit le bicomplexe , extension naturelle du complexe engendré par un ensemble simplicial . Ceci permet de définir la notion de ruban de base un cycle de . La somme directe de l’homologie des colonnes de contient, outre l’homologie de , des groupes dans lesquels se trouvent les obstructions à l’existence de rubans. Si est un sous-ensemble simplicial, stable par subdivision, de l’ensemble des simplexes singuliers d’un espace topologique, l’existence de rubans entraîne l’invariance...
Compacta with the shape finite complexes
Computing immersed normal surfaces in the figure-eight knot complement.
Correction to "Locally flat 2-spheres in simply connected 4-manifolds".