Dr. Katz DEq Homework Solutions 11

# Dr. Katz DEq Homework Solutions 11 - Algebraic Solutionsof...

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Algebraic Solutionsof Differential Equations 11 (1.2.2) Interior Product and Cup Product. Let us now recall the morphism I of interior product for each integer v=>l. (1.2.2.1) I: Hom~x(~, cg) _, Hom~,,(A~, C~| ~). In terms of local sections fl, ... ,fv of ~ and q~ of Hom(o~, ~), v (1.2.2.2) I((p)(fx A... A f~)= ~ (- 1) j-1 q~(fj)Qfx ^"" ^ fj ^"" ^ f~. j=l (1.2.2.3) Proposition. The diagram Extl(.~,,ff) av Exfl(A~,ff| 14 ~ (x, Horn (~, ~)) -~-' , ~1 (X, Horn (A" ~, .~ | A v-1 ~)) in which the vertical isomorphisms are (1.2.1.8) and (1.2.1.8 bis), is com- mutative. Proof. Just as in (1.2.1.9), let us choose a covering V~ of X and sections qh: ~1V~-, o~1V~ of ~: ~-,o~ Abusing notation, we denote by A v qh the composition (1.2.2,3.1)
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