Abstract
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.
Funder
Swiss Federal Institute of Technology Zurich
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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1. A note on the integrality of volumes of representations;Proceedings of the American Mathematical Society;2023-06-30