Refined analytic torsion
نویسنده
چکیده
For a representation of the fundamental group of a compact oriented odd-dimensional manifold we define a refinement of the Ray-Singer torsion associated to this representation. If the representation is acyclic then our new invariant is a non-zero complex number, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. The refined analytic torsion is a holomorphic function of the space of acyclic representation of the fundamental group. When the representation is unitary, the absolute value of the refined analytic torsion is equal to the Ray-Singer torsion, while its phase is determined by the eta-invariant. The fact that the Ray-Singer torsion and the eta-invariant can be combined into one holomorphic function allows to use methods of complex analysis to study both invariants. I will present several applications of this method. In particular, I will calculate the ratio of the refined analytic torsion and the Turaev
منابع مشابه
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Given an acyclic representation α of the fundamental group of a compact oriented odddimensional manifold, which is close enough to an acyclic unitary representation, we define a refinement Tα of the Ray-Singer torsion associated to α, which can be viewed as the analytic counterpart of the refined combinatorial torsion introduced by Turaev. Tα is equal to the graded determinant of the odd signat...
متن کاملar X iv : m at h / 05 05 53 7 v 1 [ m at h . D G ] 2 5 M ay 2 00 5 REFINED ANALYTIC TORSION
Given an acyclic representation α of the fundamental group of a compact oriented odddimensional manifold, which is close enough to an acyclic unitary representation, we define a refinement Tα of the Ray-Singer torsion associated to α, which can be viewed as the analytic counterpart of the refined combinatorial torsion introduced by Turaev. Tα is equal to the graded determinant of the odd signat...
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