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Bounds for the genus of a
normal surface
William Jaco, Jesse Johnson, Jonathan Spreer and Stephan Tillmann |
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Geometry & Topology 20 (2016) 1625–1671
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Abstract |
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This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact orientable 3–manifold in terms of the quadrilaterals in its cell decomposition — different bounds arise from varying hypotheses on the surface or triangulation. Two applications of these bounds are given. First, the minimal triangulations of the product of a closed surface and the closed interval are determined. Second, an alternative approach to the realisation problem using normal surface theory is shown to be less powerful than its dual method using subcomplexes of polytopes. |
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Dedicated to Hyam Rubinstein on the occasion of his 65\textitth birthday |
Keywords
3–manifold, normal surface, minimal triangulation,
efficient triangulation, realisation problem
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Mathematical Subject Classification 2010
Primary: 57N10
Secondary: 57Q15, 57M20, 57N35, 53A05
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References |
Publication
Received: 24 November 2014
Accepted: 17 July 2015
Published: 4 July 2016
Proposed: Cameron Gordon
Seconded: David Gabai, Ronald Stern
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Authors |
| William Jaco | |
| Department of Mathematics Oklahoma State University Stillwater, OK 74078-1058 USA |
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| Jesse Johnson | |
| Mathematics Department Oklahoma State University Stillwater, OK 74078-1058 USA |
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| Jonathan Spreer | |
| School of Mathematics and
Physics The University of Queensland Brisbane, QLD 4072 Australia |
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| Stephan Tillmann | |
| School of Mathematics and
Statistics The University of Sydney Sydney, NSW 2006 Australia |
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