Related Ideas
The de Rham cohomology has inspired many mathematical ideas, including Dolbeault cohomology, Hodge theory, and the Atiyah-Singer index theorem. However, even in more classical contexts, the theorem has inspired a number of developments. Firstly, the Hodge theory proves that there is an isomorphism between the cohomology consisting of harmonic forms and the de Rham cohomology consisting of closed forms modulo exact forms. This relies on an appropriate definition of harmonic forms and of the Hodge theorem. For further details see Hodge theory.
Read more about this topic: De Rham Cohomology
Famous quotes containing the words related and/or ideas:
“A parent who from his own childhood experience is convinced of the value of fairy tales will have no difficulty in answering his child’s questions; but an adult who thinks these tales are only a bunch of lies had better not try telling them; he won’t be able to related them in a way which would enrich the child’s life.”
—Bruno Bettelheim (20th century)
“Unlike Freud, Jung did not believe that a dream is a mask for a meaning already known but deceitfully withheld from the conscious mind. In his view, dreams were communication, ideas expressed not always straightforwardly, but in the best way possible within the limits of the medium. Dreaming, in Jung’s psychology, is a constructive process.”
—Jeremy Campbell (b. 1931)