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2012 Generalized Mom-structures and ideal triangulations of $3$–manifolds with nonspherical boundary
Ekaterina Pervova
Algebr. Geom. Topol. 12(1): 235-265 (2012). DOI: 10.2140/agt.2012.12.235


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.


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Ekaterina Pervova. "Generalized Mom-structures and ideal triangulations of $3$–manifolds with nonspherical boundary." Algebr. Geom. Topol. 12 (1) 235 - 265, 2012.


Received: 17 March 2011; Revised: 24 August 2011; Accepted: 7 September 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1250.57030
MathSciNet: MR2916275
Digital Object Identifier: 10.2140/agt.2012.12.235

Primary: 57M20, 57N10
Secondary: 57M15, 57M50

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 1 • 2012
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