Within geometric topology of PL n-manifolds (with or withoutboundary), a representation theory exists, which makes use of (n+1)-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for (n+1)-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Actually,the same problem was already faced - and solved - in [FG], but for closed n-manifolds, only; here, the whole class of PL-manifolds is considered, and the up-to-date knowledge involved in the proof (i.e. shelling and bistellar operations, among all) throw a deeper light on the previous results, too. Moreover, the equivalence criterion for PL-manifolds via dipole moves is proved to be equivariant with respect to the boundary triangulation.

An equivalence criterion for PL-manifolds / Casali, Maria Rita. - In: RENDICONTI DEL SEMINARIO DELLA FACOLTÀ DI SCIENZE DELL'UNIVERSITÀ DI CAGLIARI. - ISSN 0370-727X. - STAMPA. - 72:(2002), pp. 1-17.

An equivalence criterion for PL-manifolds

CASALI, Maria Rita
2002

Abstract

Within geometric topology of PL n-manifolds (with or withoutboundary), a representation theory exists, which makes use of (n+1)-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for (n+1)-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Actually,the same problem was already faced - and solved - in [FG], but for closed n-manifolds, only; here, the whole class of PL-manifolds is considered, and the up-to-date knowledge involved in the proof (i.e. shelling and bistellar operations, among all) throw a deeper light on the previous results, too. Moreover, the equivalence criterion for PL-manifolds via dipole moves is proved to be equivariant with respect to the boundary triangulation.
2002
72
1
17
An equivalence criterion for PL-manifolds / Casali, Maria Rita. - In: RENDICONTI DEL SEMINARIO DELLA FACOLTÀ DI SCIENZE DELL'UNIVERSITÀ DI CAGLIARI. - ISSN 0370-727X. - STAMPA. - 72:(2002), pp. 1-17.
Casali, Maria Rita
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/450744
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