The so-called Mom-structures on hyperbolic cusped 3–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 3–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 3–manifold N, and ideal triangulations of N; 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 N to each other.
Keywords: $3$–manifold, triangulation, Mom-structure
Pervova, Ekaterina 1
@article{10_2140_agt_2012_12_235,
author = {Pervova, Ekaterina},
title = {Generalized {Mom-structures} and ideal triangulations of 3{\textendash}manifolds with nonspherical boundary},
journal = {Algebraic and Geometric Topology},
pages = {235--265},
year = {2012},
volume = {12},
number = {1},
doi = {10.2140/agt.2012.12.235},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.235/}
}
TY - JOUR AU - Pervova, Ekaterina TI - Generalized Mom-structures and ideal triangulations of 3–manifolds with nonspherical boundary JO - Algebraic and Geometric Topology PY - 2012 SP - 235 EP - 265 VL - 12 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.235/ DO - 10.2140/agt.2012.12.235 ID - 10_2140_agt_2012_12_235 ER -
%0 Journal Article %A Pervova, Ekaterina %T Generalized Mom-structures and ideal triangulations of 3–manifolds with nonspherical boundary %J Algebraic and Geometric Topology %D 2012 %P 235-265 %V 12 %N 1 %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.235/ %R 10.2140/agt.2012.12.235 %F 10_2140_agt_2012_12_235
Pervova, Ekaterina. Generalized Mom-structures and ideal triangulations of 3–manifolds with nonspherical boundary. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 235-265. doi: 10.2140/agt.2012.12.235
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