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The $p$-exponent of the $K(1)_*$-local spectrum $\Phi SU(n)$


Author: Michael J. Fisher
Journal: Proc. Amer. Math. Soc. 131 (2003), 3617-3621
MSC (2000): Primary 55P42
DOI: https://doi.org/10.1090/S0002-9939-03-06936-3
Published electronically: February 26, 2003
MathSciNet review: 1991776
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Abstract: Let $p$ be a fixed odd prime. In this paper we prove an exponent conjecture of Bousfield, namely that the $p$-exponent of the spectrum $\Phi SU(n)$is $(n-1) + \nu_p((n-1)!)$ for $n \geq 2$. It follows from this result that the $p$-exponent of $\Omega^{q} SU(n) \langle i \rangle$ is at least $(n-1) + \nu_p((n-1)!)$ for $n \geq 2$ and $i,q \geq 0$, where $SU(n) \langle i \rangle$ denotes the $i$-connected cover of $SU(n)$.


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

  • 1. A.K. Bousfield: Uniqueness of infinite deloopings for $K$-theoretic spaces, Pacific J. Math. 129 (1987), 1-31. MR 89g:55017
  • 2. A.K. Bousfield: Unstable localization and periodicity, In Algebraic Topology: New Trends in Localization and Periodicity, Birkhauser, Basel (1996), 33-50. MR 98c:55014
  • 3. A.K. Bousfield: The $K$-theory localizations and $v_1$-periodic homotopy groups of $H$-spaces, Topology 38 (1999), 1239-1264. MR 2000d:55022
  • 4. D.M. Davis: Odd primary $bo$-resolutions and $K$-theory localization, Illinois J. Math. 30 (1986), 79-100. MR 87g:55026
  • 5. D.M. Davis and M. Mahowald: $v_1$-localizations of finite torsion spectra and spherically resolved spaces, Topology 32 (1993), 543-550. MR 94h:55018
  • 6. L. Hodgkin: On the $K$-theory of Lie groups, Topology 6 (1967), 1-35. MR 35:4950
  • 7. F.S. Roberts: Applied Combinatorics, Prentice Hall (1984), 252-280. MR 85h:05001

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Additional Information

Michael J. Fisher
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Address at time of publication: Department of Mathematics, California State University, Fresno, 5245 North Backer Avenue M/S PB 108, Fresno, California 93740
Email: mfisher@csufresno.edu

DOI: https://doi.org/10.1090/S0002-9939-03-06936-3
Received by editor(s): October 29, 2001
Received by editor(s) in revised form: June 7, 2002
Published electronically: February 26, 2003
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society

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