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 Anomalies and analytic torsion on hyperbolic manifolds

1999 ◽  
Vol 40 (8) ◽  
pp. 4119-4133
Author(s):  
A. A. Bytsenko ◽  
A. E. Gonçalves ◽  
M. Simões ◽  
F. L. Williams
Keyword(s):  
Hyperbolic Manifolds ◽  
Analytic Torsion

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.

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