Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nilpotent spaces: some inequalities on nilpotency degrees

Author: Augusto Reynol Filho
Journal: Proc. Amer. Math. Soc. 115 (1992), 501-512
MSC: Primary 55P60; Secondary 55Q99
MathSciNet review: 1093597
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Our purpose in this work is to compare the nilpotency degree of the action of $ {\pi _1}(X)$ on $ {\pi _n}(X)\quad (2 \leq n \leq 7)$ with the one of the action of $ {\pi _1}(X)$ on $ Hn(\tilde X)$. We work in the category of the nilpotent spaces (here $ \tilde X$ means the universal cover of $ X$). The main point in the proof of the main theorems, which yields such inequalities, is the reiterated use of the Serre spectral sequence.

References [Enhancements On Off] (What's this?)

  • [H] Peter J. Hilton, On $ G$-spaces, Bol. Soc. Brasil Mat. 7 (1976), 65-73. MR 0488048 (58:7622)
  • [HMR] P. Hilton, G. Mislin, and J. Roitberg, Localization of nilpotent groups and spaces, Notas Mat., vol. 15, North Holland, Amsterdam, 1975.
  • [HRS] P. Hilton , J. Roitberg, and D. Singer, On $ G$-spaces, Serre classes, and $ G$-nilpotency, Math. Proc. Cambridge Philos. Soc. 84 (1978), 443-454. MR 0494084 (58:13015)
  • [W] George W. Whitehead, Elements of homotopy theory, Graduate Texts in Math., Springer-Verlag, New York, Heidelberg, and Berlin, 61 (1978). MR 516508 (80b:55001)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P60, 55Q99

Retrieve articles in all journals with MSC: 55P60, 55Q99

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society