Bounds for the genus of a normal surface

William Jaco; Jesse Johnson; Jonathan Spreer; Stephan Tillmann

doi:10.2140/gt.2016.20.1625

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arXiv · 1411.6413

Bounds for the genus of a normal surface

William Jaco·Jesse Johnson·Jonathan Spreer·Stephan Tillmann

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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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BibTeX RIS

William Jaco, Jesse Johnson, Jonathan Spreer, Stephan Tillmann. 2014-11-24. Bounds for the genus of a normal surface. https://doi.org/10.2140/gt.2016.20.1625

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