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By C. Allday, V. Puppe (auth.), Larry Smith (eds.)

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Additional info for Algebraic Topology Göttingen 1984: Proceedings of a Conference held in Göttingen, Nov. 9–15, 1984

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Here we use inductively the is i n t r o d u c e d in [3], in §2 are e s s e n t i a l l y de- and by the sequences of b o u n d a r y invariants [4]. 3) are r e a l i z a b l e by an a p p r o p r i a t e X. This, together with conditions on the r e a l i z a b i l i t y of h o m o l o g y homomorphisms, yields the result. 4) above is an a b b r e v i a t i o n of our result in [3], we d e s c r i b e many p r o p e r t i e s of a Remark: [4] since F-system a s s o c i a t e d to H. 5) the isomorphism ~: F b n_i(Hn) ~ H o m ( H n , F n _ i) Thus @n+l is d e t e r m i n e d by P@n+l- = bn in this case.

P r e p r i n t 4. Baues HJ: H o m o t o p y classification. 5. B r o w n EH, C o p e l a n d AH Preprint (700 pages) (300 pages) (1959) H o m o l o g y analogue of P o s t n i k o v systems. Mich Math J o u r n 6:313-330 6. Chang SC (1950) H o m o t o p y invariants and continuous mappings. Proc Roy Soc A 202: 253-263 7. 2 Chang SC (1962) O n An-polyhedra. 8. Chang SC Chin A n n of Math 3(4):515-428 (1965) S u c c e s s i v e h o m o l o g y operations and their applications. Cahiers de Top. et G e o m Diff Vol VIII:I-5 9.

3 The classification of maps between simply connected 4-dimensional polyhedra w i t h the n o t a t i o n in section §2 we can state our result on the set of h o m o t o p y classes [X,X'] where X and X' are simply connected 4-dimensional polyhedra. 9). I0) a good c h a r a c t e r i z a t i o n of the subset H,[X,X'] c Hom(H,H'). 1) 41 4. 1, (X, F213) H + > G~= [x,x'] im(Ap) +ira d(q)2) G1 = Ext(H2,~) > G2 = H4(X,FT(H~)) > + ) MI(X,X' > M2(X,X') + H, G3 = Ext(H3,ker b~) > G4 = Hom(H3,cok > b~) + ) M3(X,X') + ~ M4(X,X') 6 H [X,X' ] All functions ~ are surjective maps.

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