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.
Amendola, G. (2005). A calculus for ideal triangulations of three-manifolds with embedded arcs. MATHEMATISCHE NACHRICHTEN, 278(9), 975-994 [10.1002/mana.200310285].
A calculus for ideal triangulations of three-manifolds with embedded arcs
AMENDOLA, GENNARO
2005
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.