Codimension Two PL Embeddings of Spheres with Nonstandard Regular Neighborhoods  

作　　者：Matija CENCELJ Duan REPOV Arkadiy B.SKOPENKOV 

机构地区：[1]Institute of Mathematics Physics and Mechanics,and Faculty of Education,University of Ljubljana,P.O.Box 2964,1001 Ljubljana,Slovenia. [2]Department of Differential Geometry Faculty Of Mechanics and Mathematics,Moscow State University,Moscow 119992,Russia.

出　　处：《Chinese Annals of Mathematics,Series B》2007年第5期603-608,共6页数学年刊（B辑英文版）

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);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).

摘　　要：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）.

关 键 词：Embedding Regular neighborhood Dehn surgery Fundamental group 

分 类 号：O152[理学—数学]