The concept of regular genus extends classical concepts of surface genus and of Heegaard genus of a 3-manifold. We prove that the minimum genus among 4-coloured graphs representing 3-manifolds with boundary always corresponds to a crystallization.As a consequence, every 3-coloured graph representing the boundary of a 3-manifold M, is the boundary of a 4-coloured graph representing M and having the same regular genus.
A note on the genus of 3-manifolds with boundary / Bandieri, Paola. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - STAMPA. - 35:(1989), pp. 163-175.
A note on the genus of 3-manifolds with boundary
BANDIERI, Paola
1989
Abstract
The concept of regular genus extends classical concepts of surface genus and of Heegaard genus of a 3-manifold. We prove that the minimum genus among 4-coloured graphs representing 3-manifolds with boundary always corresponds to a crystallization.As a consequence, every 3-coloured graph representing the boundary of a 3-manifold M, is the boundary of a 4-coloured graph representing M and having the same regular genus.
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