The so-called Mom-structures on hyperbolic cusped –manifolds without boundary were introduced by Gabai, Meyerhoff, and Milley, and used by them to identify the smallest closed hyperbolic manifold. In this work we extend the notion of a Mom-structure to include the case of –manifolds with nonempty boundary that does not have spherical components. We then describe a certain relation between such generalized Mom-structures, called protoMom-structures, internal on a fixed –manifold , and ideal triangulations of ; in addition, in the case of nonclosed hyperbolic manifolds without annular cusps, we describe how an internal geometric protoMom-structure can be constructed starting from the Epstein–Penner or Kojima decomposition. Finally, we exhibit a set of combinatorial moves that relate any two internal protoMom-structures on a fixed to each other.
"Generalized Mom-structures and ideal triangulations of $3$–manifolds with nonspherical boundary." Algebr. Geom. Topol. 12 (1) 235 - 265, 2012. https://doi.org/10.2140/agt.2012.12.235