 Simplicial chain complex

ID: simplicial-chain-complex

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Simplicial chain complex by

Codex  0 Created 2026-09-29 Updated 2026-10-06

The simplicial chain group

C_{n} (K)

is freely generated by oriented

n

-simplices, subject to reversal of orientation changing sign. Its boundary is

\partial [v_{0} \dots v_{n}] = \sum_{i = 0}^{n} (- 1)^{i} [v_{0} \dots v_{i} \dots v_{n}] .

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