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Unformatted text preview: 1 ∈ C p + 1 ( M ) } of all exact pforms on M is called the coboundary group. • Both Z p ( M ) and B p ( M ) are vector spaces with real coe ﬃ cients. • Recall that the exterior derivative is a map d p : C p ( M ) → C p + 1 ( M ) such that Ker d p = Z p ( M ) and Im d p1 = B p ( M ) . • Two closed forms are said to be equivalent (or cohomologous ) if they di ﬀ er by an exact form. • The collection of all equivalence classes of closed forms is the quotient vector space H p ( M ) = Z p ( M ) / B p ( M ) called the pth de Rham cohomology group . di ﬀ geom.tex; April 12, 2006; 17:59; p. 184...
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 Spring '10
 Wong
 Geometry, Algebraic Topology, Manifold, Differential form, De Rham cohomology, RHAM COHOMOLOGY GROUPS, closed orientable manifold

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