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arXiv · 1004.0872

Normal surfaces as combinatorial slicings

Jonathan Spreer
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Abstract

We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. A focus is given to dimension 3 where slicings are normal surfaces. In the case of 2-neighborly 3-manifolds and quadrangulated slicings, a lower bound on the number of quadrilaterals of normal surfaces depending on the genus g is presented. It is shown to be sharp for infinitely many values of g. Furthermore we classify slicings of combinatorial 3-manifolds with a maximum number of edges in the slicing.

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Jonathan Spreer. 2012-03-15. Normal surfaces as combinatorial slicings. https://doi.org/10.1016/j.disc.2011.03.013

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