On the Deformation Theory of Representations of Fundamental Groups of Compact Hyperbolic 3-manifolds
نویسندگان
چکیده
WE CONSTRUCT compact hyperbolic 3-manifolds M,, M, and an irreducible representation p I : T-C, (M,) + SO(3) so that singularity of the representation variety of n,(M,) into SO(3) at pr is not quadratic. We prove that for any semi-simple Lie group G the singularity of the representation variety of sr (A4,) into G at the trivial representation is not quadratic. Copyright
منابع مشابه
Deformation of Outer Representations of Galois Group II
This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...
متن کاملDeformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملDeflection of a hyperbolic shear deformable microbeam under a concentrated load
Deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. Effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. The governing differential equations and c...
متن کاملRepresentations of Fundamental Groups of 3-manifolds into Pgl(3,c): Exact Computations in Low Complexity
In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3,C) (in particular in PSL(2,C),PSL(3,R) and PU(2, 1)). The representations are obtained by gluing decorated tetrahedra of flags as in [11, 1]. We list complete computations (giving 0-dimensional or 1-dimensional solution sets) for the first complete hyperbolic non-compact manifolds wi...
متن کاملFinite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup that is locally free but not free
The purpose of this note is to show that the collection LF of finite volume hyperbolic 3-manifolds whose fundamental groups contain a subgroup that is locally free but not free is commensurably infinite. This result is stated formally as Theorem 4.1, and gives a strong answer to a question of Kropholler given in the Problem List in Niblo and Roller [19]. Recall that two hyperbolic 3-manifolds N...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1988