scholarly journals Selberg zeta functions on odd-dimensional hyperbolic manifolds of finite volume

2015 ◽  
Vol 2015 (703) ◽  
Author(s):  
Jonathan Pfaff
Keyword(s):  
Finite Volume ◽  
Zeta Functions ◽  
Hyperbolic Manifolds

AbstractWe study Selberg zeta functions

scholarly journals Analytic torsion of complete hyperbolic manifolds of finite volume

2012 ◽  
Vol 263 (9) ◽  
pp. 2615-2675 ◽  
Author(s):  
Werner Müller ◽  
Jonathan Pfaff
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds ◽  
Analytic 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.

scholarly journals Integrality of volumes of representations

2021 ◽  
Author(s):  
Michelle Bucher ◽  
Marc Burger ◽  
Alessandra Iozzi
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds ◽  
3 Dimensional ◽  
Definition Of ◽  
Dehn Fillings

AbstractLet M be an oriented complete hyperbolic n-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [3] we show that the volume of a representation $$\rho :\pi _1(M)\rightarrow \mathrm {Isom}^+({{\mathbb {H}}}^n)$$ ρ : π 1 ( M ) → Isom + ( H n ) , properly normalized, takes integer values if n is even and $$\ge 4$$ ≥ 4 . If M is not compact and 3-dimensional, it is known that the volume is not locally constant. In this case we give explicit examples of representations with volume as arbitrary as the volume of hyperbolic manifolds obtained from M via Dehn fillings.

scholarly journals Collisions at infinity in hyperbolic manifolds

2013 ◽  
Vol 155 (3) ◽  
pp. 459-463 ◽  
Author(s):  
D. B. MCREYNOLDS ◽  
ALAN W. REID ◽  
MATTHEW STOVER
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds

AbstractFor a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of M. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont and Sisto.

Virtually spinning hyperbolic manifolds

2019 ◽  
Vol 63 (2) ◽  
pp. 305-313
Author(s):  
D. D. Long ◽  
A. W. Reid
Keyword(s):  
New York ◽  
Finite Volume ◽  
Hyperbolic Geometry ◽  
Spin Structure ◽  
Hyperbolic Manifolds ◽  
Geometric Topology ◽  
Academic Press ◽  
Finite Cover

AbstractWe give a new proof of a result of Sullivan [Hyperbolic geometry and homeomorphisms, in Geometric topology (ed. J. C. Cantrell), pp. 543–555 (Academic Press, New York, 1979)] establishing that all finite volume hyperbolic n-manifolds have a finite cover admitting a spin structure. In addition, in all dimensions greater than or equal to 5, we give the first examples of finite-volume hyperbolic n-manifolds that do not admit a spin structure.

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