1,284 research outputs found
Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds
This paper gives examples of hyperbolic 3-manifolds whose SL(2,C) character
varieties have ideal points whose associated roots of unity are not 1 or -1.
This answers a question of Cooper, Culler, Gillet, Long, and Shalen as to
whether roots of unity other than 1 and -1 occur.Comment: 12 pages, 1 figure, LaTeX2e. Minor changes, additional remarks, new
description of 2nd example. To appear in_Topology
Laminations and groups of homeomorphisms of the circle
If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that
pi_1(M) acts on a circle. Here, we show that some other classes of essential
laminations also give rise to actions on circles. In particular, we show this
for tight essential laminations with solid torus guts. We also show that
pseudo-Anosov flows induce actions on circles. In all cases, these actions can
be made into faithful ones, so pi_1(M) is isomorphic to a subgroup of
Homeo(S^1). In addition, we show that the fundamental group of the Weeks
manifold has no faithful action on S^1. As a corollary, the Weeks manifold does
not admit a tight essential lamination, a pseudo-Anosov flow, or a taut
foliation. Finally, we give a proof of Thurston's universal circle theorem for
taut foliations based on a new, purely topological, proof of the Leaf Pocket
Theorem.Comment: 50 pages, 12 figures. Ver 2: minor improvement
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