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.
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