Alphabeta MathHow statement and proof provenance work
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Finite triangulations of compact PL surfaces
Definition
A finite triangulation of a compact PL surface is a finite two-dimensional simplicial complex in which each edge is incident to one or two triangles and the link of each vertex is homeomorphic to a circle or a closed interval. Its realization is the surface; its boundary is the subcomplex formed by edges incident to one triangle and their vertices. If are the numbers of vertices, edges and triangles, its simplicial Euler characteristic is .
Definition references
Subcomplexes, closures, stars, and links in a simplicial complex — links in finite simplicial complexes.
The simplicial Euler characteristic — the alternating simplex count defining .
Depends on
Used by
Dependency tree · two levels
4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- C. P. Rourke and B. J. Sanderson, Introduction to Piecewise-Linear Topology (standard reference, not scraped)