Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3–manifolds
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Published:2020-02-12
Issue:5
Volume:148
Page:2257-2271
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ISSN:0002-9939
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Container-title:Proceedings of the American Mathematical Society
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language:en
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Short-container-title:Proc. Amer. Math. Soc.
Author:
Casella Alex,Katerba Charles,Tillmann Stephan
Abstract
Closed essential surfaces in a 3–manifold can be detected by ideal points of the character variety or by algebraic non-integral representations. We give examples of closed essential surfaces not detected in either of these ways. For ideal points, we use Chesebro’s module-theoretic interpretation of Culler-Shalen theory. As a corollary, we construct an infinite family of closed hyperbolic Haken 3–manifolds with no algebraic non-integral representation into
PSL
2
(
C
)
\textrm {PSL}_2 (\mathbb {C})
, resolving a question of Schanuel and Zhang.
Funder
Department of Industry and Science, Australian Government
Publisher
American Mathematical Society (AMS)
Subject
Applied Mathematics,General Mathematics
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