Abstract
This paper uses the notion of ℂ-symplectic chain complex and proves an explicit formula for the Reidemeister torsion of an arbitrary ℂ-symplectic chain complex in terms of intersection forms of the homologies. In applications, the formula is applied to closed manifolds and also compact manifolds with boundary by using the homologies with coefficients in complex numbers field. Moreover, an explicit formula for the Reidemeister torsion of representations from the fundamental group of a closed oriented hyperbolic surface to PSL2(ℂ) is presented in terms of the cup product of twisted cohomologies, which is related with Weil–Petersson form and thus the Thurston symplectic form. The formula is also applied to pleated surfaces.
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