Normal surfaces as combinatorial slicings

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.

18 pages, 9 figures

References in corpus (3)

• simpcomp -- A GAP toolbox for simplicial complexes
• Combinatorial properties of the K3 surface: Simplicial blowups and slicings
• Euler characteristic and quadrilaterals of normal surfaces

Cited by in corpus (5)

• simpcomp -- A GAP toolbox for simplicial complexes
• The average dual surface of a cohomology class and minimal simplicial decompositions of infinitely many lens spaces
• Bounds for the genus of a normal surface
• Simplicial blowups and discrete normal surfaces in simpcomp
• Combinatorial 3-manifolds with transitive cyclic symmetry