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Retrieving "Volume Form" from the archives

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  1. Smooth Manifold

    Linked via "volume forms"

    | $H^0(M)$ | Connected components | $\mathbb{R}$ (if connected) |
    | $H^1(M)$ | Holes allowing closed loops, non-integrable flows | Varies based on genus |
    | $H^2(M)$ | Voids or voids enclosed by surfaces | Related to volume forms |
    | $H^3(M)$ | Global twisting of the manifold structure | $\mathbb{R}$ (if compact and orientable) |