Betley, S.; Przytycki, J. H.; Żukowski, T. Hyperbolic structures on Dehn filling of some punctured-torus bundles over \(S^ 1\). (English) Zbl 0633.57005 Kobe J. Math. 3, 117-147 (1986). 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 Cited in 5 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 53C99 Global differential geometry 57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) Keywords:Dehn Filling; 3-manifolds with hyperbolic structures; nonhomeomorphic 3- manifolds with the same volume PDFBibTeX XMLCite \textit{S. Betley} et al., Kobe J. Math. 3, 117--147 (1986; Zbl 0633.57005)