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Consider a compact 3-manifold M with boundary consisting of a single torus. The papers [CS1], [CS2] and [CGLS] discuss the variety of characters of SL 2 (C) representations of π 1 (M), and some of the ways in which the topological structure of M is reflected in the algebraic geometry of the character variety. We will describe in this paper a certain affine… (More)
We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic n + 1-orbifold.
T T T T T T T T T T T T T T T Abstract It is shown that with finitely many exceptions, the fundamental group obtained by Dehn surgery on a one cusped hyperbolic 3–manifold contains the fundamental group of a closed surface.
If Γ is a finite co-area Fuchsian group acting on H 2 , then the quotient H 2 /Γ is a hyperbolic 2-orbifold, with underlying space an orientable surface (possibly with punctures) and a finite number of cone points. Through their close connections with number theory and the theory of automorphic forms, arithmetic Fuchsian groups form a widely studied and… (More)
This paper reviews the two variable polynomial invariant of knots deened using representations of the fundamental group of the knot complement into SL2C: The slopes of the sides of the Newton polygon of this polynomial are boundary slopes of incompressible surfaces in the knot complement. The polynomial also contains information about which surgeries are… (More)
We prove that any Coxeter group that is not virtually free contains a surface group. In particular if the Coxeter group is word hyperbolic and not virtually free this establishes the existence of a hyperbolic surface group, and answers in the affirmative a question of Gromov in this setting. We also discuss when Artin groups contain hyperbolic surface… (More)
We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the presence of a mild smoothness hypothesis, the existence of such real projective deformations is equivalent to the question of whether one can nontrivially deform… (More)