A new proof of a theorem of J. M. Montesinos

J. Math. Sci. Univ. Tokyo
Vol. 11 (2004), No. 3, Page 325--351.

Vigara, Rub\'en
A new proof of a theorem of J. M. Montesinos
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If $M$ denotes a closed orientable 3-manifold, a Dehn sphere $\Sigma$ \cite{Papa} in $M$ will be a 2-sphere immersed in $M$ with only double curve and triple point singularities. The sphere $\Sigma$ fills $M$ \cite{Montesinos} if it defines a cell decomposition of $M$. In \cite{Montesinos} it is proved that every closed orientable 3-manifold has a nulhomotopic filling Dehn sphere, and Johansson diagrams \cite{Johansson} of Dehn spheres are proposed as a new method for representing all closed, orientable 3-manifolds. In the present paper another proof of this theorem is given and an algorithm for obtaining Johansson diagrams of closed orientable 3-manifolds from their Heegaard diagrams is developed in detail. Some examples are given.

Mathematics Subject Classification (1991): 57N10, 57N35.
Mathematical Reviews Number: MR2097529

Received: 2003-10-29