Algebraic and geometric solutions of hyperbolic Dehn filling equations

Details Algebraic and geometric solutions of hyperbolic Dehn filling equations Algebraic and geometric solutions of hyperbolic Dehn filling equations

2003-05-05

arxiv.org/abs/math/0305077v1

A modified version is published: Topology and its Applications, 145(1-3):91--118, 2004

Mathematics

Geometric Topology

31 pages, 9 figures

Scientific paper

In this paper we study the difference between algebraic and geometric solutions of the hyperbolic Dehn filling equations for ideally triangulated 3-manifolds. We show that any geometric solution is an algebraic one, and we prove the uniqueness of the geometric solutions. Then we do explicit calculations for three interesting examples. With the first two examples we see that not all algebraic solutions are geometric and that the algebraic solutions are not unique. The third example is a non-hyperbolic manifold that admits a positive, partially flat solution of the compatibility and completeness equations.

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