"드람 코호몰로지"의 두 판 사이의 차이

2012년 8월 7일 (화) 11:16 판

한 점이 빠진 유클리드 공간 의 드람 코호몰로지
\(H_{\mathrm{dR}}^{k}(\mathbb{R}^n - \{0\})\simeq \begin{cases} \mathbb{R} & \mbox{if } k = 0,n-1 \\ 0 & \mbox{if } k \ne 0,n-1 \end{cases}\)
n=3 인 경우
\(H_{\mathrm{dR}}^{k}(\mathbb{R}^3 - \{0\})\simeq \begin{cases} \mathbb{R} & \mbox{if } k = 0,2 \\ 0 & \mbox{if } k \ne 0,2 \end{cases}\)
역제곱 벡터장 항목 참조
n=3 인 경우
\(H_{\mathrm{dR}}^{k}(\mathbb{R}^3 - \{0\})\simeq \begin{cases} \mathbb{R} & \mbox{if } k = 0,2 \\ 0 & \mbox{if } k \ne 0,2 \end{cases}\)
각원소 벡터장 항목 참조

Dr Rham-Hodge 이론
- finding a canonical representative in a given cohomology class
- 리만 다양체 구조
- 라플라시안

드람
Hodge
- Hodge decomposition
  - graduation associated to the so-called "Hodge filtration" on the differential forms of the manifold
Delbeault
- cohomology of sheaves of holomorphic forms
Kodaira
- vanishing theorem
- analytic proof of Lefschetz theorem on hyperplane sections of a projective manifold
- embedding theorem
Leray
- sheaf cohomology using fine resolutions
Grothendieck
- sheaf cohomology in algebraic geometry
Deligne
- existence of a mixed Hodge structure on the cohomology of algebraic varieties
http://www.google.com/search?hl=en&tbs=tl:1&q=
수학사연표

@@ 77번째 줄: / 77번째 줄: @@
 * http://www.amazon.com/Differential-Forms-Singular-Varieties-Mathematics/dp/0849337399
 * [http://www.math.upenn.edu/%7Esiegelch/Notes/Cattani1.pdf http://www.math.upenn.edu/~siegelch/Notes/Cattani1.pdf]
+* Variations on the de Rham Complex Michael Eastwood http://www.ams.org/notices/199911/fea-eastwood.pdf
 * Math Overflow http://mathoverflow.net/search?q=