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The top cohomology class of certain spaces. (English) Zbl 0766.55007

The author considers finite 1-connected \(CW\) complexes \(M\) admitting a Sullivan minimal model of the form: \((\Lambda(x_ 1,\dots,x_ n)\otimes\Lambda(y_ 1,\dots,y_ m),d)\) with \(| x_ i|\) even, \(| y_ i|\) odd, \(d(x_ i)=0\) and \(d(y_ i)=f_ i(x_ 1,\dots,x_ n)\). He then gives a formula for a cocycle representing the top class in terms of the matrix \((\partial f_ i/\partial x_ j)\).

MSC:

55P62 Rational homotopy theory
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[1] Cartan, H., La transgression dans un groupe de Lie dans un espace fibré principal, (Colloque de Topologie (espaces fibrés), Bruxelles 1950, Thone, Liège (1951), Mason: Mason Paris), 57-71 · Zbl 0045.30701
[2] Félix, Y.; Halperin, S., Rational L-S category and its applications, Trans. Amer. Math. Soc., 273, 1-37 (1982) · Zbl 0508.55004
[3] Félix, Y.; Halperin, S.; Thomas, J. C., Gorenstein spaces, Adv. Math., 71, 92-112 (1988) · Zbl 0659.57011
[4] Greub, W. H.; Halperin, S.; Vanstone, J. R., Connections, Curvature and Cohomology, Vol. III (1975), Academic Press: Academic Press New York
[5] Halperin, S., Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc., 230, 173-199 (1977) · Zbl 0364.55014
[6] Halperin, S., Lectures on minimal models, Mém. Soc. Math. France, 9/10 (1983) · Zbl 0536.55003
[7] Koszul, J. L., Sur un type d’algèbres differéntielles en rapport avec la transgression, (Colloque de Topologie (espaces fibrés), Bruxelles 1950, Thone, Liège (1951), Mason: Mason Paris), 73-81 · Zbl 0045.30801
[8] A. Murillo, Rational fibrations and differential homological algebra, Trans. Amer. Math. Soc., to appear.; A. Murillo, Rational fibrations and differential homological algebra, Trans. Amer. Math. Soc., to appear. · Zbl 0754.55011
[9] A. Murillo, On the evaluation map, Trans. Amer. Math. Soc., to appear.; A. Murillo, On the evaluation map, Trans. Amer. Math. Soc., to appear. · Zbl 0796.55005
[10] Sullivan, D., Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math., 269-331 (1978) · Zbl 0374.57002
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