Abstract 

Octahedral decomposition is a way to triangulate a knot complement, which was originally inspired by  Kashaev volume conjecture. This octahedral decomposition leads us another understanding about PSL(2,C)-representations of a knot complement. In this talk, we discuss reducible representations and its equivariant pseudo-developing onto $\mathbb{H}^3$ through octahedral decomposition. From the approach, a new method computing Alexander polynomial will be introduced.