Scholarlink

LetDe Rham cohomology M be a smooth manifold and let \(\Omega ^p(M,{\mathbb K})\) be the space of differential p-forms on M with values in \({\mathbb K}\) ; if \(p > \dim M\) , then \(\Omega ^p(M,{\mathbb K}) = 0\) . The exterior derivative d takes p-forms into \((p+1)\) -forms. One of the main properties of the exterior derivative is that \( d^2 = 0. \) Recall that the forms \(\varphi \) for which \(d \varphi = 0\) are called closed and those of the form \(\psi = d \varphi \) - exact.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Chern, Pontrjagin, and Euler Classes of Vector Bundles

  • 章节

  • 发表日期：

    2026年

查看全文
  • Johann Davidov

摘要

LetDe Rham cohomology M be a smooth manifold and let \(\Omega ^p(M,{\mathbb K})\) be the space of differential p-forms on M with values in \({\mathbb K}\) ; if \(p > \dim M\) , then \(\Omega ^p(M,{\mathbb K}) = 0\) . The exterior derivative d takes p-forms into \((p+1)\) -forms. One of the main properties of the exterior derivative is that \( d^2 = 0. \) Recall that the forms \(\varphi \) for which \(d \varphi = 0\) are called closed and those of the form \(\psi = d \varphi \) - exact.