Nilpotent spaces of sections
HTML articles powered by AMS MathViewer
- by Jesper Michael Møller
- Trans. Amer. Math. Soc. 303 (1987), 733-741
- DOI: https://doi.org/10.1090/S0002-9947-1987-0902794-3
- PDF | Request permission
Abstract:
The space of sections of a fibration is nilpotent provided the base is finite $CW$-complex and the fiber is nilpotent. Moreover, localization commutes with the formation of section spaces.References
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573, DOI 10.1007/978-3-540-38117-4
- Herbert Federer, A study of function spaces by spectral sequences, Trans. Amer. Math. Soc. 82 (1956), 340–361. MR 79265, DOI 10.1090/S0002-9947-1956-0079265-2
- André Haefliger, Rational homotopy of the space of sections of a nilpotent bundle, Trans. Amer. Math. Soc. 273 (1982), no. 2, 609–620. MR 667163, DOI 10.1090/S0002-9947-1982-0667163-8
- R. O. Hill Jr., Moore-Postnikov towers for fibrations in which $\pi _{1}$(fiber) is non-abelian, Pacific J. Math. 62 (1976), no. 1, 141–148. MR 410747, DOI 10.2140/pjm.1976.62.141
- Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Mathematics Studies, No. 15, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0478146
- Peter Hilton, Guido Mislin, Joseph Roitberg, and Richard Steiner, On free maps and free homotopies into nilpotent spaces, Algebraic topology (Proc. Conf., Univ. British Columbia, Vancouver, B.C., 1977) Lecture Notes in Math., vol. 673, Springer, Berlin, 1978, pp. 202–218. MR 517093
- Dale Husemoller, Fibre bundles, 2nd ed., Graduate Texts in Mathematics, No. 20, Springer-Verlag, New York-Heidelberg, 1975. MR 0370578
- L. L. Larmore and E. Thomas, On the fundamental group of a space of sections, Math. Scand. 47 (1980), no. 2, 232–246. MR 612697, DOI 10.7146/math.scand.a-11886
- Irene Llerena, Localization of fibrations with nilpotent fibre, Math. Z. 188 (1985), no. 3, 397–410. MR 771993, DOI 10.1007/BF01159184
- James F. McClendon, Obstruction theory in fiber spaces, Math. Z. 120 (1971), 1–17. MR 296943, DOI 10.1007/BF01109713
- J. F. McClendon, Higher order twisted cohomology operations, Invent. Math. 7 (1969), 183–214. MR 250302, DOI 10.1007/BF01404305
- Jesper Michael Møller, Spaces of sections of Eilenberg-Mac Lane fibrations, Pacific J. Math. 130 (1987), no. 1, 171–186. MR 910659, DOI 10.2140/pjm.1987.130.171
- Jesper Michael Møller and Martin Raussen, Rational homotopy of spaces of maps into spheres and complex projective spaces, Trans. Amer. Math. Soc. 292 (1985), no. 2, 721–732. MR 808750, DOI 10.1090/S0002-9947-1985-0808750-6
- C. A. Robinson, Moore-Postnikov systems for non-simple fibrations, Illinois J. Math. 16 (1972), 234–242. MR 298664, DOI 10.1215/ijm/1256052280
- Flavio E. A. da Silveira, Rational homotopy theory of fibrations, Pacific J. Math. 113 (1984), no. 1, 1–34. MR 745592, DOI 10.2140/pjm.1984.113.1
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 303 (1987), 733-741
- MSC: Primary 55P60; Secondary 55S45
- DOI: https://doi.org/10.1090/S0002-9947-1987-0902794-3
- MathSciNet review: 902794