Homotopy characterization of weakly flat knots
Polyhedral-shape concordance implying homeomorphic complements
Certain continua in with homeomorphic complements have the same shape
Concordance of compacta
Stable shape concordance implies homeomorphic complements
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.
Page 1