We give a simple alternative proof of the representation theorem of all genus two 3-manifolds by a 6-parameter family of integers, due to casali and Grasselli (Discrete Math. 87 (1991)). Our approach is different from that of the quoted paper, and it is based on the concept of extended Heegaard diagram. This permits to obtain new topological meanings of the arithmetic conditions which the parameters must satisfy for representing closed manifolds. Applications on homology spheres of genus 2 complete the paper.

Graphs encoding 3-manifolds of genus 2 / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 308:2-3(2008), pp. 308-318. [10.1016/j.disc.2006.11.044]

Graphs encoding 3-manifolds of genus 2

CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2008

Abstract

We give a simple alternative proof of the representation theorem of all genus two 3-manifolds by a 6-parameter family of integers, due to casali and Grasselli (Discrete Math. 87 (1991)). Our approach is different from that of the quoted paper, and it is based on the concept of extended Heegaard diagram. This permits to obtain new topological meanings of the arithmetic conditions which the parameters must satisfy for representing closed manifolds. Applications on homology spheres of genus 2 complete the paper.
2008
308
2-3
308
318
Graphs encoding 3-manifolds of genus 2 / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 308:2-3(2008), pp. 308-318. [10.1016/j.disc.2006.11.044]
Cavicchioli, Alberto; Spaggiari, Fulvia
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/11380/310913
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact