Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mccme.ru/ium/postscript/f99/notes/vas.rafikov.ps Дата изменения: Thu Jan 23 16:43:47 2003 Дата индексирования: Sat Dec 22 23:29:25 2007 Кодировка: Поисковые слова: annular solar eclipse

A PL EMBEDDING OF THE 2­SPHERE IN R 4
WITH NON­STANDARD REGULAR NEIGHBORHOOD
Eugene Rafikov and Duџ san Repovџ s
Abstract. We construct a (non­locally flat) PL embedding S 2 ae R 4 such that the
regular neighborhood of S 2 in R 4 is not homeomorphic to S 2 \Theta D 2 . This example is
motivated by the following general problem: find conditions on a k­polyhedron K and
PL m­manifold M under which for each two homotopic embeddings f; g : K ! M ,
the regular neighborhoods in M of f(K) and g(K) are homeomorphic. Our example
is based on construction of a knot, concordant to the trivial one but (with any frame)
not Kirby­equivalent to the trivial knot with the frame 0.
Typeset by A M S­T E X
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