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
2002-01-01

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.
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
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Licenza Creative Commons
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

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/450744
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
social impact