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P.l. homeomorphic manifolds are equivalent by elementary shellings. (English) Zbl 0729.52003
It is shown that any simplicial p.l. manifold M of dimension n can be transformed into any other simplicial p.l. manifold homeomorphic to M by finitely many “elementary shellings”. Hereby elementary shellings are defined as follows: Let $$F=A\cdot B$$ be the join of two cells A, B of M such that F is an n-cell of M, and suppose A is not contained in the boundary of $$| M|$$ (set of M), but the join $${\mathcal B}(A)\cdot B$$ ($${\mathcal B}(A)$$ the boundary complex of A) is. Suppose, further dim $$A\geq 0$$, $$k:=\dim B\geq 0$$. Then $$M':=M\setminus ([{\mathcal B}(A)\cup \{A\}]\cdot B)$$ is said to be an elementary k-shelling of M.
Also a survey about results on shellings and bistellar operations is given, so that the main result is put into an appropriate frame.
Reviewer: G.Ewald (Bochum)

##### MSC:
 52B70 Polyhedral manifolds 57Q25 Comparison of PL-structures: classification, Hauptvermutung
##### Keywords:
polytopes; simplicial p.l. manifold; shellings
Full Text:
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