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On the coefficient groups of equivariant  -theory
Author:
Yimin Yang
Journal:
Trans. Amer. Math. Soc. 347 (1995), 77-98
MSC:
Primary 55N91; Secondary 19L47, 55N15, 57S15, 57S17
MathSciNet review:
1257645
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Abstract: We calculated the coefficient groups of equivariant  -theory for any cyclic group, and we proved that, for any compact Lie group, the coefficient groups can only have  -torsion. If there is any  -torsion, it is detected by  -primary finite subgroups of  . The rationalization of the coefficient groups then can be easily calculated.
- [1]
W. Burnside, Theory of groups of finite order, Cambridge Univ. Press, 1911.
- [2]
Stefan
Jackowski, Equivariant 𝐾-theory and cyclic subgroups,
Transformation groups (Proc. Conf., Univ. Newcastle upon Tyne, Newcastle
upon Tyne, 1976), Cambridge Univ. Press, Cambridge, 1977,
pp. 76–91. London Math. Soc. Lecture Note Series, No. 26. MR 0448377
(56 #6684)
- [3]
G.
Lewis, J.
P. May, and J.
McClure, Ordinary
𝑅𝑂(𝐺)-graded cohomology, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 2, 208–212. MR 598689
(82e:55008), http://dx.doi.org/10.1090/S0273-0979-1981-14886-2
- [4]
L.
G. Lewis Jr., J.
P. May, M.
Steinberger, and J.
E. McClure, Equivariant stable homotopy theory, Lecture Notes
in Mathematics, vol. 1213, Springer-Verlag, Berlin, 1986. With
contributions by J. E. McClure. MR 866482
(88e:55002)
- [5]
James
E. McClure, Restriction maps in equivariant 𝐾-theory,
Topology 25 (1986), no. 4, 399–409. MR 862427
(88f:55022), http://dx.doi.org/10.1016/0040-9383(86)90019-4
- [6]
Ryszard
L. Rubinsztein, Restriction of equivariant 𝐾-theory to
cyclic subgroups, Bull. Acad. Polon. Sci. Sér. Sci. Math.
29 (1981), no. 5-6, 299–304 (English, with
Russian summary). MR 640476
(83a:55008)
- [7]
G. B. Segal, Equivariant
 -theory, Publ. Math. Inst. Hautes Étude Sci. 34 (1968), 129-151.
- [8]
Jean-Pierre
Serre, Linear representations of finite groups,
Springer-Verlag, New York, 1977. Translated from the second French edition
by Leonard L. Scott; Graduate Texts in Mathematics, Vol. 42. MR 0450380
(56 #8675)
- [1]
- W. Burnside, Theory of groups of finite order, Cambridge Univ. Press, 1911.
- [2]
- Stefan Jackowski, Equivariant
 -theory and cyclic subgroups, London Math. Soc. Lecture Notes Ser., vol. 26, Cambridge Univ. Press, 1977, pp. 76-91. MR 0448377 (56:6684)
- [3]
- G. Lewis, J. P. May, and J. E. McClure, Ordinary
 -graded cohomology, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 208-212. MR 598689 (82e:55008)
- [4]
- G. Lewis, Jr., J. P. May, and M. Steinberg (with contributions by J. E. McClure), Equivariant stable homotopy theory, Lecture Notes in Math., vol. 1213, Springer-Verlag, 1986. MR 866482 (88e:55002)
- [5]
- James E. McClure, Restriction maps in equivariant
 -theory, Topology 25 (1986), 399-409. MR 862427 (88f:55022)
- [6]
- Ryszard L. Rubinsztein, Restriction of equivariant
 -theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981, no. 5-6). MR 640476 (83a:55008)
- [7]
- G. B. Segal, Equivariant -theory, Publ. Math. Inst. Hautes Étude Sci. 34 (1968), 129-151.
- [8]
- J.-P. Serre, Linear representations of finite groups, Springer-Verlag, 1977. MR 0450380 (56:8675)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1995-1257645-1
PII:
S 0002-9947(1995)1257645-1
Article copyright:
© Copyright 1995 American Mathematical Society
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