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).
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 ...