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Hyperbolic structures on Dehn filling of some punctured-torus bundles over \(S^ 1\). (English) Zbl 0633.57005

The authors generalize a construction of W. Thurston [“The geometry and topology of 3-manifolds”, mimeographed notes, Princeton Univ. (1980)]. Thurston enumerated all 3-manifolds with hyperbolic structures which may be obtained by (Dehn) filling the boundary of \(M_{\phi}^ a \)punctured torus bundle over \(S^ 1\) with monodromy map \(\phi =\left[ \begin{matrix} 1\\ 0\end{matrix} \begin{matrix} 1\\ 1\end{matrix} \right]\left[ \begin{matrix} 1\\ 1\end{matrix} \begin{matrix} 0\\ 1\end{matrix} \right]\in SL(2,{\mathbb{R}})\) \((M_{\phi}\) is the complement of the knot 4). The authors do the same for certain other \(\phi\), and by so doing are able to demonstrate the existence of 2 nonhomeomorphic 3-manifolds with the same volume.
Reviewer: L.Neuwirth

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
53C99 Global differential geometry
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
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