Normal surfaces as combinatorial slicings

作者：Spreer Jonathan^*

来源：Discrete Mathematics, 2011, 311(14): 1295-1309.

DOI：10.1016/j.disc.2011.03.013

• Normal surface
• Slicing
• Combinatorial manifold
• Weakly neighborly polyhedral map
• Heegaard genus
• Combinatorial Heegaard splitting

We investigate slicings of combinatorial manifolds as properly embedded co-dimension 1 submanifolds. Focus is given to the case of dimension 3, where slicings are (discrete) normal surfaces. For the cases of 2-neighborly 3-manifolds as well as quadrangulated slicings, lower bounds on the number of quadrilaterals of slicings depending on its genus g are presented. These are shown to be sharp for infinitely many values of g. Furthermore, we classify slicings of combinatorial 3-manifolds which are weakly neighborly polyhedral maps.

• 出版日期2011-7-28