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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
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