Canonical neighborhoods for topologically embedded polyhedra
Robert Craggs · Transactions of the American Mathematical Society · 1972
D. R. McMillan has shown that in any neighborhood of a compact two sided surface in a 3 3 -manifold there is a closed neighborhood of the surface which is the sum of a solid homeomorphic to the cartesian product of the surface with the unit interval and some small disjoint cubes-with-handles each of which intersects the cartesian product in a disk on its boundary. In the present paper the author generalizes this notion of canonical neighborhood so that it applies to topological embeddings of arbitrary polyhedra in 3 3 -manifolds. This is done by replacing the cartesian products by small regular neighborhoods of polyhedral approximations to the topological embeddings.