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$1$–efficient
triangulations and the index of a cusped hyperbolic
$3$–manifold
Stavros Garoufalidis, Craig D Hodgson, J Hyam Rubinstein and Henry Segerman |
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Geometry & Topology 19 (2015) 2619–2689
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Abstract |
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In this paper we will promote the 3D index of an ideal triangulation of an oriented cusped –manifold (a collection of –series with integer coefficients, introduced by Dimofte, Gaiotto and Gukov) to a topological invariant of oriented cusped hyperbolic –manifolds. To achieve our goal we show that (a) admits an index structure if and only if is –efficient and (b) if is hyperbolic, it has a canonical set of –efficient ideal triangulations related by – and – moves which preserve the 3D index. We illustrate our results with several examples. |
Keywords
ideal triangulations, hyperbolic $3$–manifolds, gluing
equations 3D index, invariants, $1$–efficient
triangulations
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Mathematical Subject Classification 2010
Primary: 57N10, 57M50
Secondary: 57M25
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References |
Publication
Received: 30 October 2013
Accepted: 9 January 2015
Published: 20 October 2015
Proposed: Cameron Gordon
Seconded: Peter Teichner, Robion Kirby
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Authors |
| Stavros Garoufalidis | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 USA |
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| http://www.math.gatech.edu/~stavros | |
| Craig D Hodgson | |
| Department of Mathematics and
Statistics The University of Melbourne Melbourne, Parkville VIC 3010 Australia |
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| http://www.ms.unimelb.edu.au/~cdh/ | |
| J Hyam Rubinstein | |
| Department of Mathematics and
Statistics The University of Melbourne Melbourne, Parkville VIC 3010 Australia |
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| http://www.ms.unimelb.edu.au/~rubin | |
| Henry Segerman | |
| Department of Mathematics Oklahoma State University Stillwater, VIC 74078 USA |
Department of Mathematics and
Statistics The University of Melbourne Melbourne, Parkville VIC 3010 Australia |
| http://math.okstate.edu/people/segerman/ | |
