A bound for the representability of large numbers by ternary by Golubeva E.P. PDF

By Golubeva E.P.

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Additional info for A bound for the representability of large numbers by ternary quadratic forms and nonhomogeneous waring equations

Example text

Xo Xo, Vg], [x0 A then 0 Xo j: V 0 Xo A -+ Y, A X 0 ax, fiber j w lifts = jw. HD(f,pO,p) __* Y and t h e t o be an H-map i s f s e t i n i t s simplest form general, f HD(f,p,,,p): = Fiber g , This A Hence w l i f t s t o w: X implies t h a t o b s t r u c t i o n for = - gf could be considered as t h e s e t with t h e denominator s u b s e t i d e n t i f i e d t o a point. In x0, ”1 [Wl i s a group a c t i n g on [xo xo’ vgl A and could be considered as an element o f t h e o r b i t s e t .

Xyp Y: k)T. Let Then aY kE)A]A. ’ - X -+ a: X x Let ax -+? be Q X be given by x 1 c o r e l E, Ya - 1 c o r e l p 1’ Pro of : aY = [ P p ( i a(*,x) = (x,x). x k)T][E kE) = Pp[PD(l x = Pp[PD(l x 1) x G : p ( x~ i)(1 x A ) Let 2: P[p(D x G: 1)(1 x A x x - x - p1 x PD(1 x kE)A]A = kE](1 x 1 ] ( 1 x A ) ( l x kE)A (a: x v re1 a +PX yields Fpl. ’ i s a homotopy is a c o n s t a n t p a t h and = x,* H-deviation and H-homotopy equivalence PEe(1 x = ) A : aY - 1 corel E. 4. implies - - Ya 1 corel p p - - Ya a As (p, i s a homotopy equivalence p2)~.

4. Actions, H-actions and p r i n c i p a l f i b r a t i o n s The notions of a c t i o n s and p r i n c i p a l f i b r a t i o n s used i n t h e category of t o p o l o g i c a l spaces can be adapted t o t h e homotopy category s o t h a t some o f t h e homotopy p r o p e r t i e s of t h e t o p o l o g i c a l models a r e preserved. This can be done i n v a r i o u s ways. , A d e t a i l e d study of such a d a p t a t i o n s i n [ S t a ~ h e f f ] ~[ S, t a s h e f f ] 5' [Fuchs] and [ P o r t e r I 2 .

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A bound for the representability of large numbers by ternary quadratic forms and nonhomogeneous waring equations by Golubeva E.P.


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