Combinatorial and arithmetic identities based on formal group laws

  • Andrew Baker
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1298)

Abstract

We define generalised Bernoulli and Stirling numbers based on a formal group law, and investigate some of their properties; in particular we give analogues of the classical "Kummer congruences". As a sample application we use these to compute some products and Massey products in the cohomology of a certain universal "Hopf algebroid", which arises in algebraic topology as the Adams-Novikov E2-term.

AMS Mathematics Subject Classification (1980)

Primary 14L05, 55N22 Secondary 10A40, 55T15 

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References

  1. [1]
    J.F. Adams, "On the groups J(X) — IV", Topology 5 (1966) 21–71.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    S. Araki, "Typical formal groups in complex cobordism and K-theory", Lecture Notes in Mathematics, Kinokinuya Book Store (1974).Google Scholar
  3. [3]
    A. Baker, "On weakly almost complex manifolds with vanishing decomposable Chern numbers", Contemporary Math., 19 (1983) 1–7.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    A. Baker, F. Clarke, N. Ray, L. Schwartz, "The stable homotopy of BU and the Kummer congruences", submitted to Ann. Math., (1986).Google Scholar
  5. [5]
    M. Hazewinkel, "Formal Groups and applications", Academic Press (1978).Google Scholar
  6. [6]
    N. Katz, "p-adic L-functions for CM fields", Invent. Math. 49 (1978).Google Scholar
  7. [7]
    The Manchester School of Topology, "Modular representations, the iterated S1-transfer, and the chromatic filtration", work in progress.Google Scholar
  8. [8]
    H.R. Miller, "Universal Bernoulli numbers and the S1-transfer", in "Current Trends in Algebraic Topology", CMS-AMS (1982) 437–49.Google Scholar
  9. [9]
    H.R. Miller, D.C. Ravenel, W.S. Wilson, "Periodic phenomena in the Adams-Novikov spectral sequence", Annals of Math. 106 (1977) 469–516.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    J. Riordan, "Combinatorial Identities", Academic Press.Google Scholar
  11. [11]
    D. Segal, "The cooperation on MU*(CP) and MU*HP) and the primitive generators", J. Pure and App. Alg., 14 (1979) 315–22.CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Andrew Baker
    • 1
  1. 1.Mathematics DepartmentManchester UniversityManchesterU.K.

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