Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds

Alex Casella; Charles Katerba; Stephan Tillmann

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arXiv · 1808.02535

Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds

Alex Casella·Charles Katerba·Stephan Tillmann

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Abstract

Closed essential surfaces in a three-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 representations into PSL(2, C), resolving a question of Shanuel and Zhang.

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BibTeX RIS

Alex Casella, Charles Katerba, Stephan Tillmann. 2018-08-07. Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds. https://arxiv.org/abs/1808.02535

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