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Better spelling "DeRham", not derham... I can't figure out how to change this... moderators? The cohomology of the complex of differential forms on a smooth manifold with differential given by exterior derivative.
8
votes
Hodge dual of de Rham cohomology and singular cohomology
The Hodge * operator action on cohomology is generally speaking
metric-dependent, hence * is not well-defined without fixing the metric.
There are some caveats. On complex curves, for example, the
Hod …