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ISSN 1088-9485(e) ISSN 0273-0979(p)

Book Review

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Book Information

Author(s): 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., $29.95, ISBN 3-7643-6605-2

References:

1.: K. Anderson, J. Grodal, J. Møller and A. Viruel, ``The classification of -compact groups for odd.'' 87 pp. (Preprint, 2003).
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 -modules and equivariant mod 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 via -actions. I.'' Ann. of Math. (2) 135 (1992), no. 1, 183-226. MR 93e:55019a
10.: J. Lannes, ``Sur la cohomologie modulo des -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 -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

Additional Information:

Reviewer(s):
J. P. C. Greenlees
Affiliation: University of Sheffield
Email: j.greenlees@sheffield.ac.uk

Review Information:
Journal: Bull. Amer. Math. Soc. 41 (2004), 369-376.

MSC (2000): Primary 20J05; Secondary 20J06, 14F35, 55U10
PII: S 0273-0979(04)01012-2
Posted: February 24, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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