NJ Wildberger Lecture Series : Simplicial Complex (单纯 復形)

Simplex : 单纯 (plural Simplices)
0-dim (Point) \triangle_0
1-dim (Line) \triangle_1
2-dim (Triangle) \triangle_2
3-dim (Tetrahedron) \triangle_3

Simplicial Complex: 单纯復形 built by various Simplices under some rules.

Definitions of Simplex : S (v_0, v_1, ..., v_n)
Face
Orientation
Boundary (\delta )
\displaystyle \boxed { \delta(S) = \sum_{i=0}^{n} (-1)^i (v_0 ...\hat v_i ...v_n)}

image

Theorem: \boxed { \delta ^2 (S) = 0} SO SIMPLE !!!

Follow the entire Algebraic Topology from University of New South Wales (3rd / 4th Year Math) :

Algebraic Topology: a beginner’s course – N J Wildberger:

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