| Abstract: | Refining the notion of an ideal triangulation of a compact three‐manifold, we provide in this paper a combinatorial presentation of the set of pairs (M,α), where M is a three‐manifold and α is a collection of properly embedded arcs. We also show that certain well‐understood combinatorial moves are sufficient to relate to each other any two refined triangulations representing the same (M,α). Our proof does not assume the Matveev–Piergallini calculus for ideal triangulations, and actually easily implies this calculus. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
