Mom technology and hyperbolic 3-manifolds

Details Mom technology and hyperbolic 3-manifolds Mom technology and hyperbolic 3-manifolds

2009-10-27

arxiv.org/abs/0910.5043v1

Mathematics

Geometric Topology

27 pages, 8 figures; to appear in the Proceedings of the 2008 Ahlfors-Bers Colloquium (AMS Contemporary Mathematics series)

Scientific paper

This is an expository paper on Mom-technology, describing the recent work of the authors in this area (found in arXiv:math/0606072, arXiv:0705.4325, and arXiv:0809.0346) concerning the use of Mom-technology to find the minimum-volume compact hyperbolic 3-manifold and the 10 smallest cusped hyperbolic 3-manifolds. In addition we provide a survey of a selection of results on volumes of hyperbolic 3-manifolds, and a discussion of outstanding open problems in this area.

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