Lambda-Rings

The following sections are included:

• Preface

• Contents

The following sections are included:

• Symmetric Functions
  • Symmetric functions in two sets of variables

• λ-Rings
  • The λ-ring Z
  • Basic properties of λ-rings
  • Examples of λ-rings
  • Homomorphisms and ideals
  • Augmented λ-rings

• Free λ-Rings
  • The free λ-ring on one generator

• The Verification Principle

• The Splitting Principle

• Exercises

The following sections are included:

• The Universal λ-Ring Λ(R)
  • Λ(R) is a ring
  • Λ(R) is a λ-ring

• Categories and Functors
  • Categories
  • Functors
  • Natural transformations

• Comonads and Coalgebras
  • Comonads
  • Coalgebras

• λ-Rings as Λ-Coalgebras

• Exercises

The following sections are included:

• Adams Operations

• γ-Operations

• γ-Filtration
  • Verification principle for γ-rings
  • Adams operations acting on the γ-filtration

• ψ-Rings

• ψ-Rings as Ψ-Coalgebras

• Wilkerson's Theorem

• Localization and Completion of λ-Rings
  • Localization of λ-rings
  • Completions of λ-rings

• Exercises

The following sections are included:

• Big Witt Vectors
  • The Witt polynomials
  • The Witt addition and multiplication

• Artin-Hasse Exponential

• Characterization of the Functor Λ
  • Analogs of the Witt polynomials

• W as a Comonad
  • The polynomials Q_n,m
  • Frobenius maps on Λ(R)
  • Frobenius maps on W(R)
  • Alternative proof of (4.34)

• Exercises

The following sections are included:

• Binomial Rings as λ-Rings

• Integer-Valued Polynomials

• A Basis for Integer-Valued Polynomials

• Binomial Rings as Integer-Valued Polynomials

• Knutson's Theorem

• Necklace Rings
  • Primitive necklaces
  • Necklace polynomials
  • Relations with Λ(R)

• Exercises

The following sections are included:

• Filtered λ-Rings
  • Filtered rings
  • Filtered λ-rings
  • Filtered Wilkerson's Theorem

• Power Series Rings

• Classification of λ(Z[x]/〈x²〉)

• Classification of λ(Z[x]/〈x³〉)

• Exercises

The following sections are included:

• Power Series Rings
  • The universal ring Γ
  • The universal ψ^p
  • The bijection ζ

• Filtered λ-Rings as Coalgebras

• Exercises

The following sections are included:

• Power Series and Polynomial Rings

• Universal Ring Γ

• Representation Ring

• Topological K-Theory

• Mislin Genus

The following sections are included:

• Hints to Selected Exercises

• List of Notations

• Bibliography

• Index