Deformations of reducible SL(n,C) representations of fibered 3-manifold groups

Let $M_{\varphi }$ be a surface bundle over a circle with monodromy $\phi:S \rightarrow S$\mathrm{.}Westudydeformationsofcertainreduciblerepresentationsof$\pi_1(M_\phi)$into$$\text{SL}$(n,$\mathbb{C}$)$, obtained by composing a reducible representation into $\text{SL}(2,\mathbb{C})$ with the irreducible representation $\text{SL}(2,\mathbb{C})\to \text{SL}(n,\mathbb{C})$. In particular, we show that under certain conditions on the eigenvalues of ${\varphi }^{\ast }$, the reducible representation is contained in a $(n+1+k)(n-1)$ dimensional component of the representation variety, where $k$ is the number of components of $\mathrm{\partial }{M}_{\varphi }$. This result applies to mapping tori of pseudo-Anosov maps with orientable invariant foliations whenever 1 is not an eigenvalue of the induced map on homology, where the reducible representation is also a limit of irreducible representations.