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Book Review

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Book Information:

Authors: W. G. Dwyer and H.-W. Henn
Title: Homotopy theoretic methods in group cohomology
Additional book information: Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser, Basel, 2001, x + 98 pp., ISBN 3-7643-6605-2, $29.95

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

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  • 2. C. Broto, R. Levi and R. Oliver, ``The homotopy theory of fusion systems.'' J. Amer. Math. Soc. 16 (2003), no. 4, 779-856.
  • 3. G. Carlsson, ``G. B. Segal's Burnside ring conjecture for $( Z/2)\sp{k}$.'' Topology 22 (1983), no. 1, 83-103. MR 84a:55007
  • 4. W.G. Dwyer, J.P.C. Greenlees and S. Iyengar, ``Duality in algebra and topology.'' (Preprint, 2002), 39 pp.
  • 5. W.G. Dwyer, H.R. Miller, and C.W. Wilkerson, ``The homotopic uniqueness of $BS\sp 3$.'' Algebraic topology, Barcelona, 1986, 90-105, Lecture Notes in Math., 1298, Springer, Berlin, 1987. MR 89e:55019
  • 6. W.G. Dwyer and C.W. Wilkerson, ``Homotopy fixed-point methods for Lie groups and finite loop spaces.'' Ann. of Math. (2) 139 (1994), no. 2, 395-442. MR 95e:55019
  • 7. H.-W. Henn, J. Lannes and L. Schwartz, ``Localizations of unstable $A$-modules and equivariant mod $p$ cohomology.'' Math. Ann. 301 (1995), no. 1, 23-68. MR 95k:55036
  • 8. S. Jackowski and J.E. McClure, ``Homotopy approximations for classifying spaces of compact Lie groups.'' Algebraic topology (Arcata, CA, 1986), 221-234, Lecture Notes in Math., 1370, Springer, Berlin, 1989. MR 90m:55012
  • 9. S. Jackowski, J.E. McClure and R. Oliver, ``Homotopy classification of self-maps of $BG$ via $G$-actions. I.'' Ann. of Math. (2) 135 (1992), no. 1, 183-226. MR 93e:55019a
  • 10. J. Lannes, ``Sur la cohomologie modulo $p$ des $p$-groupes abéliens élémentaires.'' Homotopy theory (Durham, 1985), 97-116, London Math. Soc. Lecture Note Ser., 117, Cambridge Univ. Press, Cambridge, 1987. MR 89e:55037
  • 11. J. Lannes, ``Sur les espaces fonctionnels dont la source est le classifiant d'un $p$-groupe abélien élémentaire.'' With an appendix by Michel Zisman. Inst. Hautes Études Sci. Publ. Math. No. 75 (1992), 135-244. MR 93j:55019
  • 12. R. Levi, ``On homological rate of growth and the homotopy type of $\Omega BG\sp \wedge\sb p$.'' Math. Z. 226 (1997), no. 3, 429-444. MR 98k:55016
  • 13. H.R. Miller, ``The Sullivan conjecture on maps from classifying spaces.'' Ann. of Math. (2) 120 (1984), no. 1, 39-87. MR 85i:55012
  • 14. D.G. Quillen, ``The spectrum of an equivariant cohomology ring. I, II.'' Ann. of Math. (2) 94 (1971), 549-572; ibid. (2) 94 (1971), 573-602. MR 45:7743
  • 15. D.L. Rector, ``Loop structures on the homotopy type of $S\sp{3}$.'' Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle, Wash., 1971), pp. 99-105, Lecture Notes in Math., Vol. 249, Springer, Berlin, 1971. MR 49:3916

Review Information:

Reviewer: J. P. C. Greenlees
Affiliation: University of Sheffield
Email: j.greenlees@sheffield.ac.uk
Journal: Bull. Amer. Math. Soc. 41 (2004), 369-376
MSC (2000): Primary 20J05; Secondary 20J06, 14F35, 55U10
Published electronically: February 24, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society