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

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 نشر من قبل Charles Katerba
 تاريخ النشر 2018
  مجال البحث
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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 Chesebros 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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