Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the coefficient groups of equivariant $ K$-theory


Author: Yimin Yang
Journal: Trans. Amer. Math. Soc. 347 (1995), 77-98
MSC: Primary 55N91; Secondary 19L47, 55N15, 57S15, 57S17
DOI: https://doi.org/10.1090/S0002-9947-1995-1257645-1
MathSciNet review: 1257645
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We calculated the coefficient groups of equivariant $ K$-theory for any cyclic group, and we proved that, for any compact Lie group, the coefficient groups can only have $ 2$-torsion. If there is any $ 2$-torsion, it is detected by $ 2$-primary finite subgroups of $ G$. The rationalization of the coefficient groups then can be easily calculated.


References [Enhancements On Off] (What's this?)

  • [1] W. Burnside, Theory of groups of finite order, Cambridge Univ. Press, 1911.
  • [2] Stefan Jackowski, Equivariant $ K$-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 $ RO(G)$-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 $ K$-theory, Topology 25 (1986), 399-409. MR 862427 (88f:55022)
  • [6] Ryszard L. Rubinsztein, Restriction of equivariant $ K$-theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981, no. 5-6). MR 640476 (83a:55008)
  • [7] G. B. Segal, Equivariant $ K$-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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55N91, 19L47, 55N15, 57S15, 57S17

Retrieve articles in all journals with MSC: 55N91, 19L47, 55N15, 57S15, 57S17


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1257645-1
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society