Cohen, F. R.; Taylor, L. R. Homology of function spaces. (English) Zbl 0621.55005 Math. Z. 198, No. 3, 299-316 (1988). We compute the homology of the space of pointed maps from X to Y under certain conditions on X and Y. One such set of conditions is that X be the suspension of a connected finite CW complex and that Y be the m-fold suspension of a connected CW complex, with \(m\geq\) (dimension of \(X+\) the connectivity of \(X+2).\) Under these conditions, the space Map\((X,Y)\) has the mod p homology of a product of spaces \(\Omega ^ iY\), the i-fold loops of Y. If we choose a basis for the mod p homology of X, there is one copy of \(\Omega ^ iY\) for each basis element of \(H_ i(X;F_ p)\). Under the above conditions, the homology of \(\Omega ^ iY\) is known, so this really does give a calculation of \(H_ *(\text{Map}(X,Y);F)\) for any field F. Cited in 3 Documents MSC: 55N99 Homology and cohomology theories in algebraic topology 55P40 Suspensions 54C35 Function spaces in general topology 55P35 Loop spaces Keywords:homology of the space of pointed maps; suspension of a connected finite CW complex; i-fold loop space PDFBibTeX XMLCite \textit{F. R. Cohen} and \textit{L. R. Taylor}, Math. Z. 198, No. 3, 299--316 (1988; Zbl 0621.55005) Full Text: DOI EuDML References: [1] Bott, R., Samelson, H.: On the Pontrjagin product in the space of paths. Comment. Math. Helv.27, 320-337 (1953) · Zbl 0052.19301 · doi:10.1007/BF02564566 [2] Campbell, H.E.A., Cohen, F.R., Peterson, F.P., Selick, P.S.: The space of maps of Moore spaces into spheres (in print) · Zbl 0699.55005 [3] Cohen, F.R., Lada, T.J., May, J.P.: The homology of iterated loop spaces. Lecture Notes in Math.533. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0334.55009 [4] Cohen, F.R., Moore, J.C., Neisendorfer, J.A.: Torsion in homotopy groups. Ann. Math.104, 128-168 (1979) · Zbl 0405.55018 [5] Cohen, F.R., Neisendorfer, J.A.: A construction ofp-localH-spaces. Algebraic Topology Aarhus 1982. Lecture Notes in Math.1051, pp. 351-359. Berlin-Heidelberg-New York: Springer 1984 [6] Cohen, F.R., Taylor, L.R.: The homology of function spaces. Proceedings of the Northwestern Homotopy Theory Conference. Contemp. Math.19, 39-50 (1983) · Zbl 0518.55004 [7] James, I.M.: Reduced product spaces. Ann. Math.62, 170-197 (1955) · Zbl 0064.41505 · doi:10.2307/2007107 [8] Jacobson, N.: Lie Algebras. New York: Dover 1962 · Zbl 0121.27504 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.