Half-density volumes of representation spaces of some 3-manifolds and their application (Q679042)

Half-density volumes of the irreducible SU(2)-representation space of Seifert manifolds and graph manifolds are computed. The tangent space of the irreducible SU(2)-representation space at an element \(V\) is the first homology of the underlying 3-manifold with twisted coefficients in \(V\). The half density is essentially given by the determinant term of the Reidemeister torsion of the underlying 3-manifold with coefficients in \(V\). The main tool is cutting and pasting and the sum formula of Reidemeister torsion due to Milnor and exploiting the fiber structure of a Seifert manifold. These computations are motivated by Witten's work on computing symplectic volume of the irreducible SU(2)-representation space of a Riemannian surface in terms of Reidemeister torsion and the invariant due to Jeffrey and Weitsman.