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

ISBN-10: 3540160612

ISBN-13: 9783540160618

ISBN-10: 3540397450

ISBN-13: 9783540397458

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H i l t o n P$(1965) H o m o t o p y theory and duality. G o r d o n and Breach Science Publishers, Inc. 16. H i r z e b r u c h F, N e u m a n n WD, Koh SS forms. Dekker, New York, (1971) D i f f e r e n t i a b l e m a n i f o l d s and quadratic 120 pages 55 17. K a n M D (1960) H o m o t o p y groups, commutators, and r-groups. Illinois J M a t h 4: I-8 18. S c h m i d t genden T (1984) Berechnung (n+2)-dimensionalen Universit6t 19. S h i r a i w a K der H o m o t o p i e k a t e g o r i e Polyeder der (n-l)-fach f~r n > 3.

Cahiers de Top. et G e o m Diff Vol VIII:I-5 9. C h o w S-K (1964) C o h o m o l o g y o p e r a t i o n s and h o m o t o p y type II. Scienta Sinica Vol XIII 7 : 1 0 3 3 - 1 0 4 3 10. Dold A, T h o m R (1958) Q u a s i f a s e r u n g e n und u n e n d l i c h e s y m m e t r i s c h e Produkte. Ann of Math 67:239-281 ii. F r e e d m a n MH (1982) The topology of four d i m e n s i o n a l manifolds. J Diff G e o m 17: 357-453 12. Henn HW (1983) K l a s s i f i k a t i o n n z e d r i g d i m e n s i o n a l e r p - l o k a l e r Spektren.

We show t h a t F 4 depends For the c o m p u t a t i o n of the c l a s s i f y i n g z4 which p o s s i b l y b 4 6 H o m ( H 4 , r H 2) and on the e x t e n s i o n carry a b e l i a n functor respectively. X') In §3 b e l o w we compute (b 4, the image H,[X,X'] ~2 Then exact the r - t o r s i o n sequence " O T h e n we get the s e q u e n c e > FD >> FA , ~i = ([I,i],-I ~ d ) with 1 = identity on C ~2 = (F(d) , [d,l]) with I = identity on D , FT(A) is ( 2. 1) 38 We h a v e cok(~2) ET(A) It is e a s y can be FT(A Here via = ker = A * ~/2 @ B) natural F~(A) Here For = functor formulas in A.

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Algebraic Topology Göttingen 1984: Proceedings of a Conference held in Göttingen, Nov. 9–15, 1984 by C. Allday, V. Puppe (auth.), Larry Smith (eds.)


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