Normal surfaces as combinatorial slicings

Details Normal surfaces as combinatorial slicings Normal surfaces as combinatorial slicings

2010-04-06

arxiv.org/abs/1004.0872v2

Jonathan Spreer. Normal surfaces as combinatorial slicings. Discrete Math., 311(14):1295-1309, 2011

Mathematics

Combinatorics

18 pages, 9 figures

Scientific paper

10.1016/j.disc.2011.03.013

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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