Stable orders of stunted lens spaces mod $2^v$
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- by Huajian Yang PDF
- Proc. Amer. Math. Soc. 125 (1997), 2743-2751 Request permission
Abstract:
Let $L_{2n-1}^{2n+2m}$ be the stunted lens space mod $2^v$ and $|L_{2n-1}^{2n+2m}|$ its stable order. If $v=1$, then $|L_{2n-1}^{2n+2m}|$ was determined by H. Toda (1963). In this paper, we determine the number $|L_{2n-1}^{2n+2m}|$ for $v\geq 2$.References
- J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603β632. MR 139178, DOI 10.2307/1970213
- J. F. Adams, A periodicity theorem in homological algebra, Proc. Cambridge Philos. Soc. 62 (1966), 365β377. MR 194486, DOI 10.1017/s0305004100039955
- Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics, vol. 121, Academic Press, Inc., Orlando, FL, 1986. MR 860042
- Teiichi Kobayashi and Masahiro Sugawara, Note on $\textrm {KO}$-rings of lens spaces mod $2^{r}$, Hiroshima Math. J. 8 (1978), no.Β 1, 85β90. MR 485765
- Akie Tamamura and Susumu KΓ΄no, On the $K\textrm {O}$-cohomologies of the stunted lens spaces, Math. J. Okayama Univ. 29 (1987), 233β244 (1988). MR 936748
- Mark Mahowald, The metastable homotopy of $S^{n}$, Memoirs of the American Mathematical Society, No. 72, American Mathematical Society, Providence, R.I., 1967. MR 0236923
- R. M. Switzer, Algebraic Topology-Homotopy and Homology, Springer-Verlag Berlin Heidelberg (1978)
- Hirosi Toda, Order of the identity class of a suspension space, Ann. of Math. (2) 78 (1963), 300β325. MR 156347, DOI 10.2307/1970345
- George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508
Additional Information
- Huajian Yang
- Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
- Address at time of publication: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
- Email: hy02@lehigh.edu, yangh@icarus.math.mcmaster.ca
- Received by editor(s): May 25, 1995
- Received by editor(s) in revised form: March 13, 1996
- Communicated by: Thomas G. Goodwillie
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2743-2751
- MSC (1991): Primary 55N15, 55P25, 55T15
- DOI: https://doi.org/10.1090/S0002-9939-97-03904-X
- MathSciNet review: 1397001