Combinatorial proofs of the Lambda algebra basis and EHP sequence
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Abstract:
Combinatorial proofs are given of the $\Lambda$ basis and EHP sequence.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
- M. G. Barratt, F. Cohen, B. Gray, M. Mahowald, and W. Richter, Two results on the $2$-local $EHP$ spectral sequence, Proc. Amer. Math. Soc. 123 (1995), no. 4, 1257–1261. MR 1246514, DOI 10.1090/S0002-9939-1995-1246514-4
- A. K. Bousfield, E. B. Curtis, D. M. Kan, D. G. Quillen, D. L. Rector, and J. W. Schlesinger, The $\textrm {mod}-p$ lower central series and the Adams spectral sequence, Topology 5 (1966), 331–342. MR 199862, DOI 10.1016/0040-9383(66)90024-3
- A. K. Bousfield and D. M. Kan, Pairings and products in the homotopy spectral sequence, Trans. Amer. Math. Soc. 177 (1973), 319–343. MR 372860, DOI 10.1090/S0002-9947-1973-0372860-2
- A. K. Bousfield, Homotopy spectral sequences and obstructions, Israel J. Math. 66 (1989), no. 1-3, 54–104. MR 1017155, DOI 10.1007/BF02765886
- J. M. Boardman and B. Steer, On Hopf invariants, Comment. Math. Helv. 42 (1967), 180–221. MR 221503, DOI 10.1007/BF02564417
- Edward B. Curtis and Mark Mahowald, The unstable Adams spectral sequence for $S^3$, Algebraic topology (Evanston, IL, 1988) Contemp. Math., vol. 96, Amer. Math. Soc., Providence, RI, 1989, pp. 125–162. MR 1022678, DOI 10.1090/conm/096/1022678
- Edward B. Curtis, Some nonzero homotopy groups of spheres, Bull. Amer. Math. Soc. 75 (1969), 541–544. MR 245007, DOI 10.1090/S0002-9904-1969-12236-6
- Edward B. Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971), 107–209 (1971). MR 279808, DOI 10.1016/0001-8708(71)90015-6
- Mizuho Hikida, Some acyclic relations in the lambda algebra, Hiroshima Math. J. 34 (2004), no. 2, 147–160. MR 2086839
- 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
- I. M. James, On the suspension sequence, Ann. of Math. (2) 65 (1957), 74–107. MR 83124, DOI 10.2307/1969666
- S. O. Kochman, Bordism, stable homotopy and Adams spectral sequences, Fields Institute Monographs, vol. 7, American Mathematical Society, Providence, RI, 1996. MR 1407034, DOI 10.1090/fim/007
- Wên Hsiung Lin, Algebraic Kahn-Priddy theorem, Pacific J. Math. 96 (1981), no. 2, 435–455. MR 637982
- 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
- 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
- Mark Mahowald, The image of $J$ in the $EHP$ sequence, Ann. of Math. (2) 116 (1982), no. 1, 65–112. MR 662118, DOI 10.2307/2007048
- Mark Mahowald and Robert D. Thompson, The fiber of the secondary suspension map, Amer. J. Math. 116 (1994), no. 1, 179–205. MR 1262430, DOI 10.2307/2374985
- Stewart B. Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970), 39–60. MR 265437, DOI 10.1090/S0002-9947-1970-0265437-8
- 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
- William Richter, The $H$-space squaring map on $\Omega ^3S^{4n+1}$ factors through the double suspension, Proc. Amer. Math. Soc. 123 (1995), no. 12, 3889–3900. MR 1273520, DOI 10.1090/S0002-9939-1995-1273520-6
- William Richter, A homotopy-theoretic proof of Williams’s metastable Poincaré embedding theorem, Duke Math. J. 88 (1997), no. 3, 435–447. MR 1455528, DOI 10.1215/S0012-7094-97-08818-9
- Paul Selick, $2$-primary exponents for the homotopy groups of spheres, Topology 23 (1984), no. 1, 97–99. MR 721456, DOI 10.1016/0040-9383(84)90029-6
- 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
- Martin C. Tangora, Generating Curtis tables, Algebraic topology (Proc. Conf., Univ. British Columbia, Vancouver, B.C., 1977) Lecture Notes in Math., vol. 673, Springer, Berlin, 1978, pp. 243–253. MR 517096
- Hirosi Toda, Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N.J., 1962. MR 0143217
- John S. P. Wang, On the cohomology of the $\textrm {mod}-2$ Steenrod algebra and the non-existence of elements of Hopf invariant one, Illinois J. Math. 11 (1967), 480–490. MR 214065
Additional Information
- William Richter
- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- Received by editor(s): May 2, 2008
- Received by editor(s) in revised form: September 12, 2008
- Published electronically: January 6, 2009
- Communicated by: Ronald A. Fintushel
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2471-2482
- MSC (2000): Primary 55T15, 55Q40, 55Q25
- DOI: https://doi.org/10.1090/S0002-9939-09-09763-9
- MathSciNet review: 2495284