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Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3-manifolds
- Publication Year :
- 2018
-
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.<br />Comment: 9 pages, 1 figure. Version 2 includes internally referenced ancillary files
- Subjects :
- Mathematics - Geometric Topology
57M27
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1808.02535
- Document Type :
- Working Paper