Codimension two PL embeddings of spheres with non-trivial regular neighborhoods
by
Arkady Skopenkov
Kolmogorov College
Coauthors: Dusan Repovs (University of Ljubljana)

For a polyhedron K subset M the notation R_M(K) denotes a regular neighborhood of K in M. We study the following problem: find all pairs (m, k) such that if K is a compact k-polyhedron and M a PL m-manifold, then R_M(fK) =~ R_M(gK), for each two homotopic PL embeddings f, g:K --> M. We prove that R_S^k+2(S^k)\not =~ S^k×D², if  a) k >= 2 and S^k subset S^k+2 is the suspension over a locally flat PL knot S^k-1 subset S^k+1 such that \pi₁(S^k+1-S^k-1)\not =~ Z, or  b) k >= 3 and a PL k-sphere S^k subset S^k+2 has an isolated non-locally flat point with the singularity S^k-1 subset S^k+1 such that \pi₁(S^k+1-S^k-1)\not =~ Z.

Date received: January 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadw-12.