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.
