Strasbourg Master Class on Geometry

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pp: 371–404

DOI: 10.4171/105-1/7

Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs

Carlo Petronio[1]

(1) Università di Pisa, Italy

This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on various 3-dimensional topological “objects” (cusped manifolds, manifolds with boundary, links, graphs, orbifolds). It also exposes the classification techniques based on hyperbolic geometry and the experimental classification results of several classes of 3-dimensional topological “objects” obtained over the time.

Keywords: Hyperbolic geometry, 3-manifold, knot, link, graph