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By Roy Douglas (auth.), Peter Hoffman, Renzo A. Piccinini, Denis Sjerve (eds.)

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Extra info for Algebraic Topology: Proceedings, University of British Columbia, Vancouver, August 1977

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Stasheff, Obstructions to homotopy equivalences, Advances in Math (to appear). J. Hilton, On the h0motopy groups of a union of s~heres, J. London Math. Soc. 30(1955) 154-171. [8] T. Jozefiak, Tate resolutions for commutative graded algebras over a local ring, Fund. Math. 74 (1972) 209-231. [9] D. Quillen, Rational homotopy theory, Ann. of Math 90 (1969), 20S-29So [i0]. D. Sullivan, Infinitesinal computations in topology, preprint, 1975 [ii] C. Watkiss, Thesis, University of Tornoto, 1976. [12] M.

T Y = (Tf) ¢ of tangent (f*TX), vectors that = (~f) ¢ f * ( T X ¢ T'X) . by : X ~ X bundle; then ~TX continuous Constant mappings . If I : X ~ E is t h e i n v e r s e e set o f o - s t r u c t u r e s the trivial id u E d(R)) E' ¢ T ' X of The : X ~ X by structuring to that properties. id ; in particular, :Y ~ X) = T Y = TE = ~ of t h e the vector-bundle mapping (f . or nullhomotopic by structuring TX @ T'X d(f) is w e l l - d e - ~ T ' X = ~*E® ~ * ( T X ¢ T'X) distinction. , to a s m o o t h T'X if of the vector-bundle and elementary .

The "standard construction" C G commutative eoalgebra on s - I G w i t h C G is (additively) dual to A s - i O defined by extending d +~[ , = ~om ( < H ~ ,Q). The differential ~ is ] in the obvious way. d(e)^¢ Indeed , in fact being degreewise For example 9(0) = d(O) v(e^¢)= is the free a mixed differential ~. isomorphic to A s -I Q * where 0 " graded Lie + e ^ a ¢ + 1/2 [e,¢] 27 Define the homology HD G L ( @ ) =H(¢(~,9) and the cohomology HDGL( ~ ) = HCHom (C 0 ' Q)' 9*) Now a p e r t u r b a t i o n D o f d almost induces a c o a l g e b r a m a p ~ : ~(1)=l+s by -I p + s -1p A s -i p + s -I pA s -i p ^ s -I p + ...

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