Dr. Katz DEq Homework Solutions 11

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Algebraic Solutions of 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. ( I: Hom~x(~, cg) _, Hom~,,(A~, C~| ~). In terms of local sections fl, . .. ,fv of ~ and q~ of Hom(o~, ~), v ( I((p)(fx A. .. A f~)= ~ (- 1) j-1 q~(fj)Qfx ^"" ^ fj ^"" ^ f~. j=l ( 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 ( and ( bis), is com- mutative. Proof. Just as in (, 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)
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.

Ask a homework question - tutors are online