Equivariant acyclic maps

Authors:
Amiya Mukherjee and Aniruddha C. Naolekar

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3747-3752

MSC (1991):
Primary 55N25, 55N91

MathSciNet review:
1415334

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we apply a recently developed new version of the Bredon-Illman cohomology theory to obtain an equivariant analogue of a result of Kan and Thurston, which implies that a connected CW-complex has the homotopy type of a space obtained by applying the plus construction of Quillen to certain Eilenberg-MacLane spaces.

**1.**A. Jon Berrick,*An approach to algebraic 𝐾-theory*, Research Notes in Mathematics, vol. 56, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR**649409****2.**Glen E. Bredon,*Equivariant cohomology theories*, Lecture Notes in Mathematics, No. 34, Springer-Verlag, Berlin-New York, 1967. MR**0214062****3.**Tammo tom Dieck,*Transformation groups*, de Gruyter Studies in Mathematics, vol. 8, Walter de Gruyter & Co., Berlin, 1987. MR**889050****4.**Emmanuel Dror,*Acyclic spaces*, Topology**11**(1972), 339–348. MR**0315713****5.**A. D. Elmendorf,*Systems of fixed point sets*, Trans. Amer. Math. Soc.**277**(1983), no. 1, 275–284. MR**690052**, 10.1090/S0002-9947-1983-0690052-0**6.**D. M. Kan and W. P. Thurston,*Every connected space has the homology of a 𝐾(𝜋,1)*, Topology**15**(1976), no. 3, 253–258. MR**0413089****7.**Sören Illman,*Equivariant singular homology and cohomology. I*, Mem. Amer. Math. Soc.**1**(1975), no. issue 2, 156, ii+74. MR**0375286****8.**A. Mukherjee and G. Mukherjee,*Bredon-Illman cohomology with local coefficients*, Quart. J. Math. Oxford(2)**47**(1996), 199-219. CMP**96:15****9.**Daniel Quillen,*Cohomology of groups*, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 47–51. MR**0488054**

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Additional Information

**Amiya Mukherjee**

Affiliation:
School of Mathematics, SPIC Science Foundation, 92, G. N. Chetty Road, Madras 600 017, India

Email:
amiya@isical.ernet.in

**Aniruddha C. Naolekar**

Affiliation:
School of Mathematics, SPIC Science Foundation, 92, G. N. Chetty Road, Madras 600 017, India

Email:
anirudha@ssf.ernet.in

DOI:
http://dx.doi.org/10.1090/S0002-9939-97-04069-0

Keywords:
Equivariant cohomology,
$G$-acyclic map,
$G$-homotopy equivalence

Received by editor(s):
October 16, 1995

Received by editor(s) in revised form:
July 19, 1996

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1997
American Mathematical Society