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

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Additional resources for Algebraic Topology: Proceedings, University of British Columbia, Vancouver, August 1977

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E. d(O) = d O -(-I)Po d. This is the cohomology referred to. The class of d 2 is in H 21 (Der (AZ,d)). 26 Now look at the next term. d2d 2 = 0e H 42(Der) This says D 2 = 0 implies If d2d 2 = 0, the Massey-Lie product is defined and it vanishes iff there is a choice of d 3 for which a d 4 exists. [The only / reference I know to such Massey-Lie products is Douady, Seminarire H. ] Now the above description smacks of a spectral sequence. It is helpful to study the underlying gadget. Schlessinger pushed me into this by claiming there is a versal deformation, one from which all others can be induced.

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. Gerstenhaber, On the deformation of rings and algebras, I-V, Annals of Math 79(1964) 59-103; 84(1966) 1-19: 88(1968) 1-34; 99 (1974) 257-276; preprint with C.

Douglas, Homotopy types within a rational homotopy type, Topology 13 (1974), 209-214. K. M. Gugenheim, "On PL DeRham theory and rational homotopy type", Memoirs of the Amer. Math. Soc. 197, 1976. [s] P. Griffiths, J. Morgan and D. Su]livan, The real homotopy theory of K~hler manifolds, Inventiones Math 29(1975) p. 245-254. L. Dupont, Simplicial deRham zohomolo~y and characteristic classes of flat bundles, Topology 15 (1976) 233-245. M. P. May, On the theory and applications of differential torsion products, Mem.

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