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2016 Bounds for the genus of a normal surface
William Jaco, Jesse Johnson, Jonathan Spreer, Stephan Tillmann
Geom. Topol. 20(3): 1625-1671 (2016). DOI: 10.2140/gt.2016.20.1625

Abstract

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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William Jaco. Jesse Johnson. Jonathan Spreer. Stephan Tillmann. "Bounds for the genus of a normal surface." Geom. Topol. 20 (3) 1625 - 1671, 2016. https://doi.org/10.2140/gt.2016.20.1625

Information

Received: 24 November 2014; Accepted: 17 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1350.57024
MathSciNet: MR3523065
Digital Object Identifier: 10.2140/gt.2016.20.1625

Subjects:
Primary: 57N10
Secondary: 53A05, 57M20, 57N35, 57Q15

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.20 • No. 3 • 2016
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