The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed 5-manifolds up to piecewise-linear (PL) homeomorphism. For this, we use the combinatorial approach to the topology of PL manifolds by means of a special kind of edge-colored graphs, called crystallizations. Within this representation theory, Bracho and Montejano introduced in 1987 a nonnegative numerical invariant, called the reduced complexity, for any closed n-dimensional PL manifold. Here we obtain the complete classification of all closed connected smooth 5-manifolds of reduced complexity less than or equal to 20. In particular, this gives a combinatorial characterization of S2×S3 among closed connected spin PL 5-manifolds.

On reduced complexity of closed piecewise linear 5-manifolds / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: PERIODICA MATHEMATICA HUNGARICA. - ISSN 0031-5303. - (2021), pp. 1-15. [10.1007/s10998-020-00375-6]

On reduced complexity of closed piecewise linear 5-manifolds

Cavicchioli Alberto
;
Spaggiari Fulvia
2021

Abstract

The goal of this paper is to give some theorems which relate to the problem of classifying combinatorial (resp. smooth) closed 5-manifolds up to piecewise-linear (PL) homeomorphism. For this, we use the combinatorial approach to the topology of PL manifolds by means of a special kind of edge-colored graphs, called crystallizations. Within this representation theory, Bracho and Montejano introduced in 1987 a nonnegative numerical invariant, called the reduced complexity, for any closed n-dimensional PL manifold. Here we obtain the complete classification of all closed connected smooth 5-manifolds of reduced complexity less than or equal to 20. In particular, this gives a combinatorial characterization of S2×S3 among closed connected spin PL 5-manifolds.
2021
8-feb-2021
1
15
On reduced complexity of closed piecewise linear 5-manifolds / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: PERIODICA MATHEMATICA HUNGARICA. - ISSN 0031-5303. - (2021), pp. 1-15. [10.1007/s10998-020-00375-6]
Cavicchioli, Alberto; Spaggiari, Fulvia
File in questo prodotto:
File Dimensione Formato  
VQR_Cavicchioli-Spaggiari2021_Article_OnReducedComplexityOfClosedPie.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 777.65 kB
Formato Adobe PDF
777.65 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
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/11380/1234644
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact