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By L. P. Hughston, R. S. Ward

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In order to obtain a cohomological inter- pretation for the results mentioned in I, II, and III, it is necessary to " ::' introduce several sheaves on twistor space(5): O{n) :r: the sheaf of germs of holomorphic functions which are hom{n). the sheaf of germs of primed spinor-valued holomorphic functions, hom(n). 0A{n) the sheaf of germs of unprimed spinor-valued holomorphic functions, hom(n). the sheaf of germs of unprimed spinor-valued holornorphic functions which are hom{n-1) and satisfy ~AfA = O.

241 - 315 . Strea ter . F. & Wightman , A. S . ;;;'- • •. -'. Penrose, R. & Benjami n: New Vork. :. 2 HliSTOR FUNCTIONS AND SHEAF COHOMOLOGY by R. l properties of a hlistor functio n f(ZCt ) , to be used for ~eneratin9 a zero rest-mass field :'A' . 2 r ' A' .. • , K(X) (211 0 - ? c: x ""fA 2 ~ ! 'x ". I'" , 2 L' f (2 " ) d r. 2) (nm' under the Poincan~ t~listoY' space )101- gr oup , nor the lorentz gr oup) . (in There is a "gauge" freedom G \·/hereby fl>f-th -t-h+, where h' is hoIomorphic on some extended (iomain O~ ( ::> D) of twistor space in ~Ihich the contour 'I can be deformed to a pO i nt (to the "left" in V and to the "ri9ht" in V+ : see Fi9 , A) .

R. C. ; . Morro~l, Rossi,~. ,'·· '~" . It.... · t. ~.. ':j: ·v,rl •. ,- Prentice-Hall. J . Kodaira. K. Penrose. R. 1965 1975a eds. '" 1971 '-"-7,1. '--, . Holt, Rinehart & Winston. ~ .. • , • ... J. Isham. R. \-1. Sciama , pp. 268- 407. Clarendon: Oxford . Penrose. R. ,:' 7 '",'':(! {l';':;" '::;><1:: Weizslicker. pp . 129-145 . Prent ice - Ha 11. 36 eds. In: L Castell, -:0;" '. t, Or'ieschner & C. F. von §2 . 3. 1. J . Wooditoul3e that zero·re st ·mass fields on '~inkO\"lski equivalence classes of I-forms on twist~r show hO,"1 one can go directly from these time fields, and back again.

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