Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideal points of character varieties, algebraic non-integral
  representations, and undetected closed essential surfaces in 3-manifolds   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.

37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics