Codimension Two Pl Embeddings of Spheres with Nonstandard Regular Neighborhoods
نویسنده
چکیده
Abstract. For a given polyhedron K ⊂ M the notation RM (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 RM (fK) ∼= RM (gK), for each two homotopic PL embeddings f, g : K → M . We prove that R Sk+2 (S) 6∼= S × D for each k ≥ 2 and some PL sphere S ⊂ S (even for any PL sphere S ⊂ S having an isolated non-locally flat point with the singularity S ⊂ S such that π1(S k+1 − S) 6∼= Z).
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