Generalized Mom-structures and ideal triangulations of 3–manifolds with nonspherical boundary

Pervova, Ekaterina

doi:10.2140/agt.2012.12.235

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Generalized Mom-structures and ideal triangulations of $3$–manifolds with nonspherical boundary

Ekaterina Pervova

Algebraic & Geometric Topology 12 (2012) 235–265

DOI: 10.2140/agt.2012.12.235

Abstract

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

Mathematical Subject Classification 2010

Primary: 57M20, 57N10

Secondary: 57M15, 57M50

References

Publication

Received: 17 March 2011

Revised: 24 August 2011

Accepted: 7 September 2011

Published: 25 February 2012

Authors

Ekaterina Pervova
Dipartimento di Matematica Applicata University of Pisa Via F Buonarroti 1C I-56127 Pisa Italy

Volume 12, issue 1 (2012)