scholarly journals Topology of an attraction domain, dynamical zeta functions and Reidemeister torsion

1997 ◽  
Vol 9 (2) ◽  
pp. 259
Author(s):  
Alexander Fel'shtyn ◽  
Violetta Pilyugina
Keyword(s):  
Zeta Functions ◽  
Attraction Domain ◽  
Reidemeister Torsion

scholarly journals Ruelle Zeta Functions of Hyperbolic Manifolds and Reidemeister Torsion

2021 ◽  
Author(s):  
Werner Müller
Keyword(s):  
Fundamental Group ◽  
General Result ◽  
Hyperbolic Manifold ◽  
Zeta Functions ◽  
Hyperbolic Manifolds ◽  
Reidemeister Torsion ◽  
Finite Dimensional ◽  
Orthogonal Representations ◽  
Ruelle Zeta Function ◽  
Complex Valued

AbstractThis paper is concerned with the behavior of twisted Ruelle zeta functions of compact hyperbolic manifolds at the origin. Fried proved that for an orthogonal acyclic representation of the fundamental group of a compact hyperbolic manifold, the twisted Ruelle zeta function is holomorphic at $$s=0$$ s = 0 and its value at $$s=0$$ s = 0 equals the Reidemeister torsion. He also established a more general result for orthogonal representations, which are not acyclic. The purpose of the present paper is to extend Fried’s result to arbitrary finite dimensional representations of the fundamental group. The Reidemeister torsion is replaced by the complex-valued combinatorial torsion introduced by Cappell and Miller.

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