As it is well-known, torus bundles over $S^1$ areidentified by means of regular integer matrices of order two (see[S]); in the present paper an algorithmic procedure is described,which allows to construct, directly from any matrix $A \in GL (2;Z)$, an edge-coloured graph representing the torus bundle$TB(A)$ associated to $A.$ As a consequence, five topologically undetected elements of Lins's catalogue of orientable 3-manifolds (see [L]) are finally recognized as torus bundles over $S^1$.
Representing and recognizing torus bundles over S1 / Casali, Maria Rita. - In: BOLETÍN DE LA SOCIEDAD MATEMÁTICA MEXICANA. - ISSN 1405-213X. - STAMPA. - 10:(0)(2004), pp. 89-105.
Representing and recognizing torus bundles over S1
CASALI, Maria Rita
2004
Abstract
As it is well-known, torus bundles over $S^1$ areidentified by means of regular integer matrices of order two (see[S]); in the present paper an algorithmic procedure is described,which allows to construct, directly from any matrix $A \in GL (2;Z)$, an edge-coloured graph representing the torus bundle$TB(A)$ associated to $A.$ As a consequence, five topologically undetected elements of Lins's catalogue of orientable 3-manifolds (see [L]) are finally recognized as torus bundles over $S^1$.
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