𝐸𝐻𝑃 spectra and periodicity. II. Λ-algebra models

Gray, Brayton

doi:10.1090/S0002-9947-1993-1152324-1

$EHP$ spectra and periodicity. II. $\Lambda$-algebra models
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Trans. Amer. Math. Soc. 340 (1993), 617-640 Request permission

Abstract:

The results of part I suggest that for small $m$, the Smith-Toda spectrum $V(m)$ can be approximated by spaces having universal mapping properties and interlocking fibrations. For each $m$, a $\Lambda$-algebra model representing the Bousfield-Kan $E\prime$ term for these spaces is constructed, and all of the ideal results are proven on the chain level.

References

A. K. Bousfield and E. B. Curtis, A spectral sequence for the homotopy of nice spaces, Trans. Amer. Math. Soc. 151 (1970), 457–479. MR 267586, DOI 10.1090/S0002-9947-1970-0267586-7
A. K. Bousfield and D. M. Kan, The homotopy spectral sequence of a space with coefficients in a ring, Topology 11 (1972), 79–106. MR 283801, DOI 10.1016/0040-9383(72)90024-9
Edward B. Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971), 107–209 (1971). MR 279808, DOI 10.1016/0001-8708(71)90015-6

Calculations of the unstable

terms for spheres

Brayton Gray, $EHP$ spectra and periodicity. I. Geometric constructions, Trans. Amer. Math. Soc. 340 (1993), no. 2, 595–616. MR 1152323, DOI 10.1090/S0002-9947-1993-1152323-X
J. R. Harper and H. R. Miller, On the double suspension homomorphism at odd primes, Trans. Amer. Math. Soc. 273 (1982), no. 1, 319–331. MR 664045, DOI 10.1090/S0002-9947-1982-0664045-2
Mark Mahowald, On the double suspension homomorphism, Trans. Amer. Math. Soc. 214 (1975), 169–178. MR 438333, DOI 10.1090/S0002-9947-1975-0438333-5
William M. Singer, The algebraic EHP sequence, Trans. Amer. Math. Soc. 201 (1975), 367–382. MR 385861, DOI 10.1090/S0002-9947-1975-0385861-7