Ω^k(M), wedge product, exterior derivative d. Stokes theorem. De Rham cohomology.
graph TD
D1["Def: Ω^k\nk-forms"]
D2["Def: Wedge ∧\nalt product"]
D3["Def: Exterior d\nd²=0"]
D4["Def: Integral ∫\norientation"]
T1["Thm: d²=0"]
T2["Thm: Stokes\n∫_M dω=∫_∂M ω"]
T3["Thm: De Rham H^k\nker d/im d"]
T4["Thm: Poincaré lemma\ndω=0⇒ω=dη locally"]
T5["Thm: H^k≅H_k dual\nmanifold"]
D1 --> D2
D2 --> D3
D3 --> D4
D3 --> T1
D4 --> T2
T1 --> T3
T2 --> T3
T3 --> T5
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 11
Frontier: math.DG