Inverse invariant theory and Steenrod operations

• Main Author: Neusel, Mara D
• Format: eBook
• Language: English
• Published: Providence, R.I American Mathematical Society 2000
• Edition: 1
• Series: Memoirs of the American Mathematical Society
• Subjects: Invariants; Steenrod algebra

This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.

Table of Contents:

• Introduction 1. The $\Delta $-theorem 2. Some field theory over the Steenrod algebra 3. The integral closure theorem and the unstable part 4. The inseparable closure 5. The embedding theorem I 6. Noetherianess, the embedding theorem II and Turkish delights 7. The Galois embedding theorem, the little imbedding theorem, and a bit more 8. The big imbedding theorem, Thom classes, Turkish delights II and the reverse Landweber-Stong conjecture
• Intro -- Contents -- Introduction -- 1. The Δ…Theorem -- 1.1 Steenrod Operations -- 1.2 The Δ…theorem, Corollaries and Examples -- 2. Some Field Theory over the Steenrod Algebra -- 2.1 Graded Fields over the Steenrod Algebra -- 2.2 Separable Extensions -- 2.3 Inseparable Extensions -- 2.4 The Vector Space of Derivations -- 3. The Integral Closure Theorem and the Unstable Part -- 3.1 Rings of Fractions and Their Unstable Part -- 3.2 The Integral Closure Theorem -- 4. The Inseparable Closure -- 4.1 The Introduction of our Exotic Animal -- 4.2 The Animal and its Properties -- 4.3 Further Properties -- 5. The Embedding Theorem I -- 5.1 A Dickson Algebra in FF(H*) -- 5.2 Preparing the Embedding Theorem apres Smith-Switzer -- 5.3 The Embedding Theorem -- 6. Noetherianess, the Embedding Theorem II and Turkish Delights -- 6.1 Noetherianess -- 6.2 Turkish Delights -- 6.3 Noetherianess II -- 7. The Galois Embedding Theorem, the Little Imbedding Theorem and A Bit More -- 7.1 The Galois Embedding Theorem -- 7.2 A Bit More -- 7.3 Uniqueness Theorems -- 7.4 The Little Imbedding Theorem -- 8. The Big Imbedding Theorem, Thom Classes, Turkish Delights II and the Reverse Landweber-Stong Conjecture -- 8.1 The Big Imbedding Theorem -- 8.2 Consequences for the Module of Derivations -- 8.3 Turkish Delights II -- 8.4 The Reverse Landweber-Stong Conjecture -- A. Technical Stuff -- A.1 Old and New Relations in the Steenrod Algebra -- A.2 The Action of the Steenrod Algebra on the Dickson Algebra -- A.3 The Fractal Property of the Dickson Algebra -- A.4 The Generalized Jacobian -- References -- Font and Typesetting Information