Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Essential maps exist from $ B{\rm U}$ to $ {\rm Coker}\, J$


Author: Mark Feshbach
Journal: Proc. Amer. Math. Soc. 97 (1986), 539-545
MSC: Primary 55N20; Secondary 55P42, 55Q55
DOI: https://doi.org/10.1090/S0002-9939-1986-0840642-5
MathSciNet review: 840642
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that $ [{\text{BU,coker}}\,J] \ne 0$ but that there are no infinite loop maps from BU to coker $ J$. The proofs involve the Segal conjecture.


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

  • [AS] M. Atiyah and G. Segal, Equivariant $ K$-theory and completion, J. Differential Geom. 3 (1969), 1-18. MR 0259946 (41:4575)
  • [C] G. Carlsson, Equivariant stable homotopy and Segal's Burnside ring conjecture, Ann. of Math. (2) 120 (1984), 189-224. MR 763905 (86f:57036)
  • [D] T. tom Dieck, Transformation groups and representation theory, Lecture Notes in Math., vol. 766, Springer-Verlag, Berlin, 1979. MR 551743 (82c:57025)
  • [F] M. Feshbach, The Segal conjecture for compact Lie groups, Topology (to appear). MR 880503 (88f:57075)
  • [F2] -, The transfer and compact Lie groups, Bull. Amer. Math. Soc. 83 (1977), 372-374. MR 0440548 (55:13422)
  • [HS] L. Hodgkin and V. Snaith, Topics in $ K$-theory, two independent contributions, Lecture Notes in Math., vol. 496, Springer-Verlag, Berlin, 1975. MR 0388371 (52:9208)
  • [L] E. Laitinen, On the Burnside ring and stable cohomotopy of a finite group, Math. Scand. 44 (1979), 37-72. MR 544579 (80k:55030)
  • [MM] I. Madsen and R. J. Milgram, The classifying spaces for surgery and cobordism of manifolds, Ann. of Math. Studies, no. 92, Princeton Univ. Press, Princeton, N.J., 1979. MR 548575 (81b:57014)
  • [R] D. Ravenal, The Segal conjecture for cyclic groups and its consequences, Amer. J. Math. 106 (1984), 415-446. MR 737779 (85g:55015)
  • [S] G. Segal, The stable homotopy of complex projective space, Quart. J. Math. Oxford Ser. (2) 24 (1973), 1-5. MR 0319183 (47:7729)
  • [Sn] V. Snaith, Algebraic cobordism and $ K$-theory, Mem. Amer. Math. Soc. No. 221 (1979). MR 539791 (80k:57060)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55N20, 55P42, 55Q55

Retrieve articles in all journals with MSC: 55N20, 55P42, 55Q55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0840642-5
Keywords: Infinite loop maps, Segal conjecture, stable cohomotopy, compact Lie group
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society