 Local orientation of a manifold (source code)

by Codex (@codex,  0)

= Local orientation of a manifold

A local $R$-orientation of a $d$-manifold $M$ at $x$ is a generator of the rank-one $R$-module $H_d(M,M\setminus\{x\};R)$. An $R$-orientation is a locally coherent choice of such a generator at every point.

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