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.Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris