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Rational homotopy of spaces of maps into spheres and complex projective spaces


Authors: Jesper Michael Møller and Martin Raussen
Journal: Trans. Amer. Math. Soc. 292 (1985), 721-732
MSC: Primary 55P62; Secondary 55P15, 58D99
DOI: https://doi.org/10.1090/S0002-9947-1985-0808750-6
MathSciNet review: 808750
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Abstract: We investigate the rational homotopy classification problem for the components of some function spaces with $ {S^n}$ or $ {\mathbf{C}}{P^n}$ as target space.


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  • [1] M. C. Crabb and W. A. Sutherland, Function spaces and Hurwitz-Radon numbers, Math. Scand. 55 (1984), 67-90. MR 769026 (86d:58014)
  • [2] H. Federer, A study of function spaces by spectral sequences, Trans. Amer. Math. Soc. 82 (1956), 340-361. MR 0079265 (18:59b)
  • [3] Y. Felix and J.-C. Thomas, Homotopie rationelle. Dualité et complémentarité des modèles, Bull. Soc. Math. Belg. Ser. A 33 (1981), 7-19. MR 682637 (84h:55010)
  • [4] A. Haefliger, Rational homotopy of the space of sections of a nilpotent bundle, Trans. Amer. Math. Soc. 273 (1982), 609-620. MR 667163 (84a:55010)
  • [5] V. L. Hansen, The homotopy problem for the components in the space of maps on the $ n$-sphere, Quart. J. Math. Oxford Ser. (3) 25 (1974), 313-321. MR 0362396 (50:14838)
  • [6] -, On spaces of maps of $ n$-manifolds into the $ n$-sphere, Trans. Amer. Math. Soc. 265 (1981), 273-281. MR 607120 (82c:55014)
  • [7] -, The homotopy groups of a space of maps between oriented closed surfaces, Bull. London Math. Soc. 15 (1983), 360-364. MR 703761 (84f:55012)
  • [8] -, Decomposability of evaluation fibrations and the brace product operation of James, Compositio Math. 35 (1977), 83-89. MR 0494104 (58:13035)
  • [9] P. Hilton, G. Mislin, J. Roitberg and R. Steiner, On free maps and free homotopies into nilpotent spaces, Algebraic Topology, Proceedings, Vancouver 1977, Lecture Notes in Math., vol. 673, Springer-Verlag, Berlin and New York, 1978. MR 517093 (80c:55007)
  • [10] J. M. Møller, On spaces of maps between complex projective spaces, Proc. Amer. Math. Soc. 91 (1984), 471-476. MR 744651 (85f:55004)
  • [11] -, On the homology of spaces of sections of complex projective bundles, Pacific J. Math. 116 (1985), 143-154. MR 769828 (86k:55019)
  • [12] D. Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205-295. MR 0258031 (41:2678)
  • [13] S. Sasao, The homotopy of $ \operatorname{Map} ({\mathbf{C}}{P^m},{\mathbf{C}}{P^n})$, J. London Math. Soc. (2) 8 (1974), 193-197. MR 0346783 (49:11507)
  • [14] D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269-331. MR 0646078 (58:31119)
  • [15] W. A. Sutherland, Path-components of function spaces, Quart. J. Math. Oxford (2) 34 (1983), 223-233. MR 698208 (84g:55019)
  • [16] D. Tauré, Homotopie rationelle: Modèles de Chen, Quillen, Sullivan, Lecture Notes in Math., vol. 1025, Springer-Verlag, New York, 1983. MR 764769 (86b:55010)
  • [17] R. Thom, L'homologie des espaces fonctionelles, Colloque de Topologie Algébrique, Louvain 1956, Thone Liège; Masson, Paris, 1957, pp. 29-39. MR 0089408 (19:669h)
  • [18] G. W. Whitehead, Elements of homotopy theory, Graduate Texts in Math., vol. 61, Springer-Verlag, Berlin and New York, 1978. MR 516508 (80b:55001)
  • [19] K. Yamaguchi, On the rational homotopy of $ \operatorname{Map} ({\mathbf{H}}{P^m},{\mathbf{H}}{P^n})$, Kodai Math. J. 6 (1983), 279-288. MR 717319 (85j:55024)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0808750-6
Keywords: Path-components of mapping spaces, minimal model, rational homotopy equivalence
Article copyright: © Copyright 1985 American Mathematical Society

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