Summary
The paper uses the fact that PL manifolds may be studied through graphs with coloured edges. The representation is given by taking the l-skeleton of the cellular subdivision dual to a suitable triangulation (minimal with respect to the vertices) of a manifold. Here we describe a very simple construction to obtain a 4-coloured graph representing a closed orientable 3-manifold from its Heegaard diagram. This construction allows us to completely classify a countable class of closed orientable 3-manifoldsM n ,n ⩾ 3, introduced by L. Neuwirth in Proc. Camb. Phil. Soc.64 (1968), 603–613. Indeed, we show thatM n is homeomorphic to the Seifert fibered space
It is also proved thatM n is the unique closed 3-manifold having the canonical 2-complex associated to the standard presentation of the Fibonacci groupF(n − 1, n) as its spine.
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Cavicchioli, A. Neuwirth manifolds and colourings of graphs. Aeq. Math. 44, 168–187 (1992). https://doi.org/10.1007/BF01830977
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DOI: https://doi.org/10.1007/BF01830977