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W and a typical price y (: SP. l The map f induces a framing of the manifold r (y) as follows : pick out a certainly orientated foundation b = (v\ . . . , vice president) for the tangent house T ( SP ) •. for every x (: r l (y) remember from web page 12 that maps the subspace Tr l (y)x to 0 and maps its orthogonal supplement Tr l (y) � isomorphically onto T(SP)y. accordingly there's a distinctive vector i w (x) (: Tr \ y); C TMx i that maps into V less than dtx ' it is going to be handy to take advantage of the notation tl:J = f*)J for the ensuing framing w l (x ) , .

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