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Rationally equivalent nilpotent groups
and spaces
Author:
Joseph Roitberg
Journal:
Proc. Amer. Math. Soc. 125 (1997), 41-45
MSC (1991):
Primary 20F18, 55P60, 55P62
MathSciNet review:
1346986
Full-text PDF Free Access
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Additional Information
Abstract: Examples are constructed of rationally isomorphic, finitely generated nilpotent groups  and  such that there are no homomorphisms  inducing rational isomorphisms. Similar examples are constructed of nilpotent, or even simply-connected, finite CW-complexes.
- 1.
Joan
L. Dyer, A nilpotent Lie algebra with nilpotent
automorphism group, Bull. Amer. Math. Soc.
76 (1970), 52–56.
MR
0249544 (40 #2789), http://dx.doi.org/10.1090/S0002-9904-1970-12364-3
- 2.
Peter
Hilton, Guido
Mislin, and Joe
Roitberg, Localization of nilpotent groups and spaces,
North-Holland Publishing Co., Amsterdam, 1975. North-Holland Mathematics
Studies, No. 15; Notas de Matemática, No. 55. [Notes on Mathematics,
No. 55]. MR
0478146 (57 #17635)
- 3.
C.
A. McGibbon and Joseph
Roitberg, Phantom maps and rational equivalences, Amer. J.
Math. 116 (1994), no. 6, 1365–1379. MR 1305869
(95j:55026), http://dx.doi.org/10.2307/2375050
- 4.
C.A. McGibbon and J. Roitberg, Phantom maps and rational equivalences, II, Bol. Soc. Mat. Mex. 37 (1992), 367-381.
- 5.
Mamoru
Mimura and Hirosi
Toda, On 𝑝-equivalences and 𝑝-universal
spaces, Comment. Math. Helv. 46 (1971), 87–97.
MR
0285007 (44 #2231)
- 6.
Jesper
Michael Møller, The normalizer of the Weyl group, Math.
Ann. 294 (1992), no. 1, 59–80. MR 1180450
(94b:55010), http://dx.doi.org/10.1007/BF01934313
- 7.
Joseph
Roitberg, Rational Lie algebras and 𝑝-isomophisms of
nilpotent groups and homotopy types, Comment. Math. Helv.
50 (1975), 1–8. MR 0365561
(51 #1813)
Joseph
Roitberg, Erratum to: “Rational Lie algebras and
𝑝-isomorphisms of nilpotent groups and homotopy types”
(Comment. Math. Helv. 50 (1975), 1–8), Comment. Math. Helv.
51 (1976), no. 3, 435–436. MR 0425959
(54 #13909)
- 8.
Joseph
Roitberg, Computing homotopy classes of phantom maps, The
Hilton Symposium 1993 (Montreal, PQ), CRM Proc. Lecture Notes,
vol. 6, Amer. Math. Soc., Providence, RI, 1994,
pp. 141–168. MR 1290588
(95f:55010)
- 9.
J. Roitberg, The Mislin genus, phantom maps and classifying spaces, Topology and its Applications 69 (1996), 83-100.
- 1.
- J.L. Dyer, A nilpotent Lie algebra with nilpotent automorphism group, Bull. Amer. Math. Soc. 76 (1970), 52-56. MR 40:2789
- 2.
- P. Hilton, G. Mislin and J. Roitberg, Localization of nilpotent groups and spaces, Notas de Matemática, North-Holland Mathematics Studies 15 (1975). MR 57:17635
- 3.
- C.A. McGibbon and J. Roitberg, Phantom maps and rational equivalences, Amer. J. Math. 116 (1994), 1365-1379. MR 95j:55026
- 4.
- C.A. McGibbon and J. Roitberg, Phantom maps and rational equivalences, II, Bol. Soc. Mat. Mex. 37 (1992), 367-381.
- 5.
- M. Mimura and H. Toda, On
 -equivalences and  -universal spaces, Comment. Math. Helv. 46 (1971), 87-97. MR 44:2231
- 6.
- J. M. Møller, The normalizer of the Weyl group, Math. Ann. 294 (1992), 59-80. MR 94b:55010
- 7.
- J. Roitberg, Rational Lie algebras and p-isomorphisms of nilpotent groups and homotopy types, Comment. Math. Helv. 50 (1975), 1-8. Erratum, ibid. 51 (1976), 435-436. MR 51:1813; MR 54:13909
- 8.
- J. Roitberg, Computing homotopy classes of phantom maps, CRM Proceedings and Lecture Notes 6 (1994), 141-168. MR 95f:55010
- 9.
- J. Roitberg, The Mislin genus, phantom maps and classifying spaces, Topology and its Applications 69 (1996), 83-100.
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Additional Information
Joseph Roitberg
Affiliation:
Department of Mathematics & Statistics, Hunter College (CUNY), 695 Park Ave., New York, New York 10021;
Department of Mathematics, Graduate School (CUNY), 33 West 42 St., New York, New York 10036
Email:
jroitber@shiva.hunter.cuny.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-97-03556-9
PII:
S 0002-9939(97)03556-9
Received by editor(s):
May 5, 1995
Received by editor(s) in revised form:
July 11, 1995
Additional Notes:
Research supported (in part) by a grant from the City University of New York PSC-CUNY Research Award Program
Communicated by:
Thomas Goodwillie
Article copyright:
© Copyright 1997 American Mathematical Society
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