Plane curves associated to character varieties of 3-manifolds

@article{Cooper1994PlaneCA,
  title={Plane curves associated to character varieties of 3-manifolds},
  author={Daryl Cooper and Marc Culler and Henri Gillet and Darren D. Long and Peter B. Shalen},
  journal={Inventiones mathematicae},
  year={1994},
  volume={118},
  pages={47-84}
}
Consider a compact 3-manifold M with boundary consisting of a single torus. The papers [CS1, CS2, CGLS] discuss the variety of characters of SL2(C) representations of zl(M), and some of the ways in which the topological structure of M is reflected in the algebraic geometry of the character variety. We will describe in this paper a certain affine algebraic curve DM which is naturally associated to the character variety of M. A basis B = {~, 9.1/} for the peripheral subgroup of M determines an… CONTINUE READING

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