Syzygies and Homotopy Theory

• Main Author: Johnson, F.E.A (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2012.
• Series: Algebra and Applications, 17
• Subjects: Mathematics.; Commutative algebra.; Commutative rings.; Group theory.; Group Theory and Generalizations.; Commutative Rings and Algebras.

The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. S...

Table of Contents:

• Preliminaries
• The restricted linear group
• The calculus of corners and squares
• Extensions of modules
• The derived module category
• Finiteness conditions
• The Swan mapping
• Classification of algebraic complexes
• Rings with stably free cancellation
• Group rings of cyclic groups
• Group rings of dihedral groups
• Group rings of quaternionic groups
• Parametrizing W1 (Z) : generic case
• Parametrizing W1 (Z) : singular case
• Generalized Swan modules
• Parametrizing W1 (Z) : G = C¥ ´ F
• Conclusion .