Year: 1971
Type: article
Abstract: Let K be a knot manifold, that is the 3-sphere S 3 minus an open regular neighborhood of a polygonal simple closed curve in S 3 .Whether K can be embedded in S s differently or in a homotopy 3-sphere different from S 3 (if such really exist) leads in a natural way to the question of which planar surfaces can be embedded in K. Geometric conditions are imposed on the embedded planar surfaces which are sufficient to imply that K is not knotted, that is K is homeomorphic to a disk cross SK 17. F. Waldhausen, On irreducible ^-manifolds which are sufficiently large, Ann. of Math., (2) 87 (1968), 56-88.18., Gruppen mit zentrum und 3-dimensionale mannigfaltigkeiten, Topology, 6 (1967), 505-517.
Source: Pacific Journal of Mathematics
Author: Howard Lambert
Institution: University of Southern California
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1997165965