Bousfield localizations of classifying spaces

of nilpotent groups

Authors:
William G. Dwyer, Emmanuel Dror Farjoun and Douglas C. Ravenel

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1855-1861

MSC (1991):
Primary 55N20, 55R35

Published electronically:
February 5, 1999

MathSciNet review:
1646308

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finitely generated nilpotent group. The object of this paper is to identify the Bousfield localization of the classifying space with respect to a multiplicative complex oriented homology theory . We show that is the same as the localization of with respect to the ordinary homology theory determined by the ring .

**[BK72]**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****[Bou79]**A. K. Bousfield,*The localization of spectra with respect to homology*, Topology**18**(1979), no. 4, 257–281. MR**551009**, 10.1016/0040-9383(79)90018-1**[Bou82]**A. K. Bousfield,*On homology equivalences and homological localizations of spaces*, Amer. J. Math.**104**(1982), no. 5, 1025–1042. MR**675308**, 10.2307/2374082**[DDK77]**E. Dror, W. G. Dwyer, and D. M. Kan,*An arithmetic square for virtually nilpotent spaces*, Illinois J. Math.**21**(1977), no. 2, 242–254. MR**0438330****[Kri]**I. Kriz. Morava K-theory of classifying spaces: some calculations.*Topology*. 36:1247-1273, 1997. CMP**97:13****[Kur56]**A. G. Kurosh,*The theory of groups. Vol. II*, Chelsea Publishing Company, New York, N.Y., 1956. Translated from the Russian and edited by K. A. Hirsch. MR**0080089**

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Additional Information

**William G. Dwyer**

Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Email:
william.g.dwyer.1@nd.edu

**Emmanuel Dror Farjoun**

Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel

Email:
farjoun@math.huji.ac.il

**Douglas C. Ravenel**

Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York 14627

Email:
drav@harpo.math.rochester.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05194-1

Received by editor(s):
September 17, 1997

Published electronically:
February 5, 1999

Additional Notes:
All three authors were partially supported by the US-Israel Binational Science Foundation, and the first and third authors by the National Science Foundation.

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 1999
American Mathematical Society