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Spun normal surfaces in
$3$–manifolds, I: $1$–efficient triangulations
Ensil Kang and Joachim Hyam Rubinstein |
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Algebraic & Geometric Topology 22 (2022) 3533–3576
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Abstract |
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Spun normal surfaces are a useful way of representing proper essential surfaces using ideal triangulations for –manifolds with tori and Klein bottle boundaries. Walsh (2011) established that proper essential surfaces which are not virtual fibers can be put into spun normal form, so long as the triangulations have no edges isotopic into the boundary. We use a different approach to study spun normal surfaces in –efficient ideal triangulations. –efficiency is a stronger condition than Walsh used, but we are able to deal with semifiber surfaces. Moreover, fiber surfaces are shown to spin normalize, so long as there is a closed normal surface in the infinite cyclic covering dual to the fibering. In two followup papers, spinning essential surfaces in general ideal triangulations will be considered and in the case of a single boundary component of the –manifold, all the boundary slopes of proper essential surfaces will be shown to occur at vertices of the projective solution space, answering a question of Dunfield and Garoufalidis. |
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Keywords
3–manifolds, normal surfaces, ideal triangulation, spun
normal surfaces
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Mathematical Subject Classification 2010
Primary: 57M99
Secondary: 57M10
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References |
Publication
Received: 1 September 2014
Revised: 19 January 2021
Accepted: 6 September 2021
Published: 14 March 2023
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Authors |
| Ensil Kang | |
| Department of Mathematics Chosun University Gwangju South Korea |
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| Joachim Hyam Rubinstein | |
| Department of Mathematics and
Statistics The University of Melbourne Melbourne VIC Australia |
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