Non-acyclic Reidemeister torsions of manifolds of odd dimension
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초록
Given an oriented closed $C^{\infty}$-manifold $M$ of odd dimension and a unitary representation $\rho : \pi_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated with $\rho$ is not acyclic. As corollaries, we introduce some topological invariants of $M$, which include non-acyclic extensions of abelian torsions and the Alexander polynomials of links. Furthermore, we propose a volume form of the $\SU(n)$-character varieties of $M$. Moreover, we compute the Reidemeister torsions of some representations of 3-manifolds and give a comparison of the works of Farber and Turaev.
Abstract
Given an oriented closed $C^{\infty}$-manifold $M$ of odd dimension and a unitary representation $\rho : \pi_1(M) \ra \GL_n(\F)$, we define a Reidemeister torsion, even if the cohomology associated with $\rho$ is not acyclic. As corollaries, we introduce some topological invariants of $M$, which include non-acyclic extensions of abelian torsions and the Alexander polynomials of links. Furthermore, we propose a volume form of the $\SU(n)$-character varieties of $M$. Moreover, we compute the Reidemeister torsions of some representations of 3-manifolds and give a comparison of the works of Farber and Turaev.