The homology groups of topological spaces have been defined in chapter 3. If a topological space is a manifold, we may define the dual of the homology groups out of differential forms defined on . The dual groups are called the de Rham cohomology groups. Besides physicists’ familiarity with differential forms, cohomology groups have several advantages over homology groups.
We follow closely Nash and Sen (1983) and Flanders (1963). Bott and Tu (1982) contains more advanced topics.
Exercise 6.2. Show that
来源与版本
正文：英文 · OCR 机器稿 · 待校对
核对状态：OCR 机器稿 · 待校对
来源版本：second-edition-local
来源 PDF SHA-256：fcd24c3371d092a8c699ccf5cf0765462924b6c48412804231076e8084b1940d
OCR 来源 SHA-256：0b6324f01172a3548cd34382e82fd8bfae574602b6b2cfaa357ba96bc2c35478
OCR 产物 SHA-256：3b151c299a6fa53f2a128a8b127ee38820256bc37a68bbbf54cbf13d6c6b6cd5