By Michèle Audin (auth.), J. Aguadé, R. Kane (eds.)

**Contents:** M. Audin: periods Caracteristiques Lagrangiennes.- A. Baker: Combinatorial and mathematics Identities in line with Formal crew Laws.- M.C. Crabb: at the sturdy Splitting of U(n) and ÛU(n).- E. Dror Farjoun, A. Zabrodsky: The Homotopy Spectral series for Equivariant functionality Complexes.- W.G. Dwyer, G. Mislin: at the Homotopy kind of the parts of map*(BS3, BS3).- W.G. Dwyer, H.R. Miller, C.W. Wilkerson: The Homotopy area of expertise of BS3.- W.G. Dwyer, A. Zabrodsky: Maps among Classifying Spaces.- B. Eckmann: Nilpotent crew motion and Euler Characteristic.- N.D. Gilbert: at the basic Catn-Group of an n-Cube of Spaces.- H.H. Glover: Coloring Maps on Surfaces.- P. Goerss, L. Smith, S. Zarati: Sur les A-Algèbres Instables.- K.A. Hardie, K.H. Kamps: The Homotopy class of Homotopy Factorizations.- L.J. Hernández: right Cohomologies and the right kind class Problem.- A. Kono, ok. Ishitoya: Squaring Operations in Mod 2 Cohomology of Quotients of Compact Lie teams by way of Maximal Tori.- J. Lannes; L. Schwartz: at the constitution of the U-Injectives.- S.A. Mitchell: The Bott Filtration of a Loop Group.- Z. Wojtkowiak: On Maps from Holim F to Z.- R.M.W. wooden: Splitting (CP x...xCP ) and the motion of Steenrod Squares Sqi at the Polynomial Ring F2 Äx1,...,xnÜ.

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**Extra info for Algebraic Topology Barcelona 1986: Proceedings of a Symposium held in Barcelona, April 2–8, 1986**

**Example text**

U,) = Ext** We r e c a l l C** where Cn* = (U,U) n = U,U e U , ' ' " nR: U, ~ U,U. tensor d: We t a k e products. C°* = U, i s t h e c o h o m o l o g y o f a c h a i n complex ® U, U*~ with and t h e t e n s o r The d i f f e r e n t i a l products are all (U,U) n ~ Here ~ (x, %, cobar denotes the right left ... e. Ys Then o f c o u r s e Ext* is a graded commutative Y-algebra. 2 cycles Z/2, if and b is odd z/12, if n = 2 if n for generators is even and greater than a n z / 2 d n, e UznU If U* construction.

To the (x,z) : > > (U(V) x collapsing Then identity. ) The a stable onto same to the map is the splitting the top cell. Pontrjagin-Thom standard tubular we o b t a i n a map onto Rn(V)/Rn-I(V) : ~(V)+ ^ ~(V) + way. neighbourhood s : identity. is the o n of the p r o j e c t i o n The general construction, the : ~(V) S ~(V) (This case Let c : identified + + ~(V) ^ 2(V) > it is i n d u c e d 3 b y (x/2 - I) (x/2 + 1 ) - l e x p ( - z ) in So s gives in the ~(V)) + = U(V) + ^ ~(V) +. Indeed, the Rn(V)/Rn-I(v) cell ~(V), (c A I)°S (0,0) of s i g n top construction at choice the = ~(V) @ and the d e r i v a t i v e same.

C. Crabb and K. Knapp, On the codegree of negative multiples the Hopf bundle (preprint, 1986). 5. T. Frankel, Critical submanifolds of the classical groups and Stiefel manifolds, in Differential and Combinatorial Topology: Symposium in Honor of Marston Morse, 37-53 (ed. S. Cairns, Princeton University Press, 1965). Theory New York, 1967). (Cambridge University On the space of matrices 6. M. James, Spaces associated with Stiefel manifolds, Math. Soc. 9 (1959), 115-40. 7. M. James, General T o p o l o g y and Homotopy Theory York, 1984).