Euler characteristic and quadrilaterals of normal surfaces

Tejas Kalelkar

doi:10.1007/s12044-008-0015-7

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arXiv · 0810.0174

Euler characteristic and quadrilaterals of normal surfaces

Tejas Kalelkar

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Abstract

Let $M$ be a compact 3-manifold with a triangulation $τ$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial description. Secondly, we obtain an inequality relating the number of normal triangles and normal quadrilaterals of $F$, that depends on the maximum number of tetrahedrons that share a vertex in $τ$.

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Tejas Kalelkar. 2008-10-01. Euler characteristic and quadrilaterals of normal surfaces. https://doi.org/10.1007/s12044-008-0015-7

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