Pacific Journal of Mathematics

The homology of a free loop space.

Stephen Halperin and Micheline Vigué-Poirrier

Article information

Source
Pacific J. Math., Volume 147, Number 2 (1991), 311-324.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102644913

Mathematical Reviews number (MathSciNet)
MR1084712

Zentralblatt MATH identifier
0712.55011

Subjects
Primary: 55P99: None of the above, but in this section
Secondary: 55N99: None of the above, but in this section 55T99: None of the above, but in this section 57R19: Algebraic topology on manifolds

Citation

Halperin, Stephen; Vigué-Poirrier, Micheline. The homology of a free loop space. Pacific J. Math. 147 (1991), no. 2, 311--324. https://projecteuclid.org/euclid.pjm/1102644913


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References

  • [1] J. F. Adams, On the cobarconstruction, Proc. Nat. Acad. Sci. U.S.A., 42 (1956), 409-412.
  • [2] J. F. Adams and P. J. Hilton, On the chain algebraof a loop space,Comment. Math. Helv., 20 (1955), 305-330.
  • [3] D. Anick, A model of Adams Hilton typefor fibre squares, Illinois J. Mati., 29 (1985), 463-502.
  • [4] D. Anick, Hopf algebras up to homotopy, J. Amer. Math. Soc, 2 (1989), 417-453.
  • [5] L. Avramov and S. Halperin, Through the looking glass,a dictionary between ra- tional homotopy theory and local algebra,pp. 3-27 in Algebra,Algebraic Topol- ogy and their Iterations, Lecture Notes in Mathematics 1183, Springer Verlag, Berlin, 1986.
  • [6] H. Baues and J.-M. Lemaire, Minimal models in homotopy theory,Math. Ann., 225(1977), 219-242.
  • [7] A. K. Bousfield and V. K. A. M. Gugenheim, On PL de Rham theory and rational homotopy type, Memoirs Amer. Math. Soc, 179 (1976).
  • [8] D. Burghelea and Z. Fiedorowicz, Cyclic homology and algebraic K-theory of spaces,Topology, 25 (1986), 303-317.
  • [9] H. Cartan, Algebres dilenberg-MacLane, Seminaire Cartan 54/55 expose 7, Oeuvres v. Ill, 1309-1394, Springer Verlag, Berlin.
  • [10] H. Cartan and S. Eilenberg, HomologicalAlgebra,PrincetonUniv. Press, Prince- ton, N.J., 1956.
  • [11] R. L. Cohen, Pseudo-isotopies,K-theory and homotopy theory, London Math. Soc, Lecture Note Series 117, Cambridge Univ. Press (1987), 35-71.
  • [12] S. Eilenberg and J. C. Moore, Homology andfibrations, Comment. Math. Helv., 40(1966), 199-236.
  • [13] M. El Haouari, P-formalite des espaces,Rapport no. 124, Universite de Lou- vain, 1987.
  • [14] Y. Felix, S. Halperin and J. C. Thomas, Gorenstein spaces, Adv. in Math., 71 (1988), 92-112.
  • [15] Y. Felix, S. Halperin, C. Jacobsson, C. Lfwall and J.-C. Thomas, The radical of the homotopy Lie algebra,Amer. J. Math., 110 (1988), 301-332.
  • [16] D. Gromoll and W. Meyer, Periodicgeodesies on compact Riemannian mani- folds, J. Differential Geom., 3 (1969), 493-510.
  • [17] V. K. A. M. Gugenheim and H. J. Munkholm, On the extendedfunctoriality of Tor and Cotor,J. Pure Appl. Algebra, 4 (1974), 9-29.
  • [18] S. Halperin, Lectures on minimal models, Memoirs Soc. Math. France, 9/10 (1984).
  • [19] J. McCleary, On the mod p Betti numbers of loop spaces, Invent. Math., 87 (1987), 643-654.
  • [20] J. McCleary and W. Ziller, On thefree loopspaceof homogeneous spaces,Amer. J. Math., 109(1987), 765-78L
  • [21] J. C. Moore, Algebre homologique et homologie des espaces classifiants, Semi- naire Cartan, 59/60, expose no. 7.
  • [22] J. C. Moore,, Differential homologicalalgebra, Actes, Congres Internat.Math., (1970), tome I, 335-339.
  • [23] D. Quillen, Rational homotopy theory, Annals of Math., 90 (1969), 205-295.
  • [24] J. E. Roos, Homology offree loopspaces,cyclichomology and rational Poincare- Betti series, preprint no. 39 (1987), Univ. of Stockholm.
  • [25] L. Smith, Homologicalalgebra and the Eilenberg-Moore spectralsequence, Trans. Amer. Math. Soc, 129 (1967), 58-93.
  • [26] L. Smith, The EMSS and the mod 2 cohomology of certainfree loopspaces, Illinois J. Math., 28 (1984), 516-522.
  • [27] D. Sullivan, Infinitesimal computations in topology, Publ. Math. I.H.E.S.(1978), 269-331.
  • [28] D. Sullivan and M. Vigue-Poirrier, The homology theory of the closed geodesic problem, J. Differential Geom., 11 (1976), 633-644.
  • [29] M. Vigue-Poirrier, Realisation de morphismes donnes en cohomologie et suite spectraled'Eilenberg-Moore, Trans. Amer. Math. Soc, 265 (1981), 447-484.
  • [30] W. Ziller, Thefree loop space on globally symmetric spaces, Invent. Math. 41 (1977), 1-22.