Mathematische Zeitschrift

, Volume 202, Issue 4, pp 493–523 | Cite as

The transfer in homological algebra

  • William M. Singer
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References

  1. 1.
    Adams, J.F.: A periodicity theorem in homological algebra. Proc. Cam. Phil. Soc.62, 365–377 (1966)Google Scholar
  2. 2.
    Adams, J.F.: Operations of then'th kind inK-theory and what we don't know aboutRP . In: New developments in topology, Segal, G. (ed.). Lond. Math. Soc. Lect. Notes Ser. no. 11, (1974)Google Scholar
  3. 3.
    Adams, J.F.: On the structure and applications of the Steenrod algebra. Commentarii Math. Helv.32, 180–214 (1958)Google Scholar
  4. 4.
    Adams, J.F.: On the non-existence of mapping off Hopf-invariant one. Ann. Math., Ser. II.72, 20–104 (1960)Google Scholar
  5. 5.
    Anderson, D.W., Davis, D.M.: A vanishing theorem in homological algebra. Commentarii Math. Helv.48, 318–327 (1973)Google Scholar
  6. 6.
    Anick, D.: On the homogeneous invariants of a tensor algebra. Preprint. (to appear)Google Scholar
  7. 7.
    Bousfield, A.K., Curtis, E.B., Kan, D.M., Reillen, D.G., Rector, D.L., Schlesinger, J.W.: The mod-p lower central series and the Adams spectral sequence. Topology5, 331–342 (1966)Google Scholar
  8. 8.
    Bousfield, A.K., Curtis, E.B.: A spectral sequence for the homotopy of nice spaces. Trans. Am. Math. Soc.151, 457–479 (1970)Google Scholar
  9. 9.
    Bruner, R.: Algebraic and geometric connecting homomorphisms in the Adams spectral sequence. In: Barratt, M.G., Mahowald, M.E. (eds.). Geometric applications of homotopy theory II. Proceedings, Evanston, 1977. (Lect. Notes Math., vol. 658, pp. 131–134 Berlin Heidelberg New York: Springer 1978Google Scholar
  10. 10.
    Carlisle, D., Eccles, P., Hilditch, S., Ray, N., Schwartz, L., Walker, G., Wood, R.: Modular representations of GL (n, p), splitting ε(CP ×CP ×...×CP ), and the β-family as framed hypersurfaces. Math. Z.189, 239–261 (1985)Google Scholar
  11. 11.
    Dickson, L.E.: A fundamental system of invariants of the general modular linear group with a solution of the form problem. Trans. Am. Math. Soc.12, 75–98 (1911)Google Scholar
  12. 12.
    Feit, W.: Characters of finite groups. Menlo Park: Benjamin 1967Google Scholar
  13. 13.
    Goerss, P., Smith, L.: Towers and injective cohomology algebras. Trans. Am. Math. Soc.303, 619–636 (1987)Google Scholar
  14. 14.
    Harris, J., Kuhn, N.: Stable decompositions of classifying spaces of finite abelianp-groups. Math. Proc. Cam. Phil. Soc.103, 427–449 (1988)Google Scholar
  15. 15.
    Hochster, M., Eagon, J.: Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci. Am. J. Math.93, 1020–1058 (1971)Google Scholar
  16. 16.
    Lin, W.H., Davis, D.M., Mahowald, M.E., Adams, J.F.: Calculation of Lin's Ext groups. Math. Proc. Cam. Phil. Soc.87, 459–570 (1980)Google Scholar
  17. 17.
    Lin, W.H.: The algebraic Kahn-Priddy theorem. Pac. J. Math.96, 435–455 (1981)Google Scholar
  18. 18.
    MacLane, S.: Homology. Ist edition, Berlin Heidelberg New York: Springer 1963Google Scholar
  19. 19.
    Mitchell, S.: Finite complexes withA(n)-free cohomology. Topology24, 227–248 (1985)Google Scholar
  20. 20.
    Mitchell, S.: SplittingB(Z/p) n andBT n via modular representation theory. Math. Z.189, 1–9 (1985)Google Scholar
  21. 21.
    Mui, H.: Modular invariant theory and the cohomology algebras of the symmetric groups. J. Fac. Sci. U. Tokyo22, 319–369 (1975)Google Scholar
  22. 22.
    Peterson, F.P.:A-generators ofP n. Unpublished lecture given at Kent State University, and at Queens University, Kingston, OntarioGoogle Scholar
  23. 23.
    Peterson, F.:A-generators for polyain polynomial algebras. Math. Proc. Cam. Phil. Soc.,105, 311–312 (1989)Google Scholar
  24. 24.
    Singer, W.M.: On the construction of certain algebras over the Steenrod algebra. J. Pure Appl. Algebra11, 53–59 (1977)Google Scholar
  25. 25.
    Singer, W.M.: On finite linear groups and the homology of the Steenrod algebra. Privately circulated MS., August, 1980Google Scholar
  26. 26.
    Singer, W.M.: Letters to Erich Ossa dated October 4, October 10, 1980Google Scholar
  27. 27.
    Singer, W.M.: A new chain complex for the homology of the Steenrod algebra. Math. Proc. Cam. Phil. Soc.90, 279–292 (1981)Google Scholar
  28. 28.
    Singer, W.M.: Invariant theory and the lambda algebra. Trans. Am. Math. Soc.280, 673–693 (1983)Google Scholar
  29. 29.
    Smith, L., Switzer, R.: Realizability and non-realizability of Dickson algebras as cohomology rings. Proc. Am. Math. Soc.89, 303–313 (1983)Google Scholar
  30. 30.
    Whitehead, G.W.: Recent advances in homotopy theory. Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics Number 5. American Mathematical Society, Providence, Rhode Island, 1970Google Scholar
  31. 31.
    Wilkerson, C.: Classifying spaces, Steenrod operations, and algebraic closure. Topology16, 227–237 (1977)Google Scholar
  32. 32.
    Wilkerson, C.: A primer on the Dickson invariants. In: Proceedings of the Northwestern Homotopy Theory Conference, Contemp. Math.19, 421–434, American Mathematical Society (1983)Google Scholar
  33. 33.
    Wood, R.M.W.: Splitting Ε(CP ×CP ×...×CP ) and the action of Steenrod squares Sqi on the polynomial ringF 2[x 1, ...,x n]. In: Anguadé, J., Kane, R. (eds.). Algebraic topology, Barcelona, 1986. (Lect. Notes Math., vol. 1298) Berlin Heidelberg New York: Springer 1987Google Scholar
  34. 34.
    Wood, R.M.W.: Steenrod squares of polynomials and the Peterson conjecture. Math. Proc. Cam. Phil. Soc.,105, 307–309 (1989)Google Scholar
  35. 35.
    Yoneda, N.: On the homology theory of modules. J. Fac. Sci., Univ. Tokyo Sect. IA,7, 193–227 (1954)Google Scholar
  36. 36.
    Yoneda, N.: Notes on products in Ext. Proc. Am. Math. Soc.9, 873–875 (1958)Google Scholar
  37. 37.
    Zarati, S., Lannes, J.: Sur les foncteurs dérivés de la déstabilisation. Math. Z.184, 25–59 (1987)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • William M. Singer
    • 1
  1. 1.Department of MathematicsFordham UniversityBronxUSA

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