Families of representations of punctured torus bundles (Q2757133)

\textit{B. Mangum} and \textit{P. Shanahan} [J. Knot Theory Ramifications 6, No. 6, 817-825 (1997; Zbl 0896.57007)] constructed a complex curve of irreducible \(SL(3,\mathbb C)\) representations of the fundamental group of a once punctured torus bundle over \(S^1\). In the present paper, following Mangum-Shanahan's recipe and using the Krammer representation of the braid group \(B_4\), a complex surface (2-parameter family) of irreducible \(SL(6,\mathbb C)\) representations of these fundamental groups is constructed (containing the curve of \(SL(3,\mathbb C)\) representations). As a corollary it is shown that almost all punctured torus bundle groups are linear. ``We hope that this complex surface contributes to an understanding of the geometry and topology of once punctured torus bundles''.