For a given polyhedron K contain M, the notation RM（K） denotes a regular neighborhood of K in M. The authors study the following problem： find all pairs （m, k） such that if K is a compact k-polyhedron and M a PL ...For a given polyhedron K contain M, the notation RM（K） denotes a regular neighborhood of K in M. The authors 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（f（K））≌RM（g（K）） for each two homotopic PL embeddings f,g ： K→M. It is proved that Rs^k＋2（Sk）≌/ S^k × D^2 for each k≥2 and some PL sphere S^k contain S^k＋2 （even for any PL sphere S^k contain S^k＋2 having an isolated non-locally flat point with the singularity S^k-1 contain S^k＋1 such that π1（S^k＋1 - S^k-1）≌/Z）.展开更多
基金Project supported by the Pierre Deligne Fund based on 2004 Balzan Prize in Mathematics,INTAS Grants(No.YSF-2002-393)the Russian Foundation for Basic Research(Nos.05-01-00993,04-01-00682,06-01-72551-NCNILa)+1 种基金President of the Russian Federation Grants(Nos.MD-3938.2005.1,NSH-1988.2003.1,MD-4729.2007.1)the Slovenian Research Agency(Nos.BI-RU/05-07-04,BI-RU/05-07-13).
文摘For a given polyhedron K contain M, the notation RM（K） denotes a regular neighborhood of K in M. The authors 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（f（K））≌RM（g（K）） for each two homotopic PL embeddings f,g ： K→M. It is proved that Rs^k＋2（Sk）≌/ S^k × D^2 for each k≥2 and some PL sphere S^k contain S^k＋2 （even for any PL sphere S^k contain S^k＋2 having an isolated non-locally flat point with the singularity S^k-1 contain S^k＋1 such that π1（S^k＋1 - S^k-1）≌/Z）.
