Lower K- and L-theory (London Mathematical Society Lecture Note Series, Series Number 178)

✍ Scribed by Andrew Ranicki

• Publisher: Cambridge University Press
• Year: 1992
• Tongue: English
• Leaves: 183
• Edition: 1
• Category: Library

✦ Synopsis

This is the first treatment in book form of the applications of the lower K- and L-groups (which are the components of the Grothendieck groups of modules and quadratic forms over polynomial extension rings) to the topology of manifolds such as Euclidean spaces, via Whitehead torsion and the Wall finiteness and surgery obstructions. The author uses only elementary constructions and gives a full algebraic account of the groups involved; of particular note is an algebraic treatment of geometric transversality for maps to the circle.

✦ Table of Contents

Contents
Introduction
§1. Projective class and torsion
§2, Graded and bounded categories
§3. End invariants
§4. Excision and transversality in lf-theory
§5. Isomorphism torsion
§6. Open cones
§7. K-theory of d(A)
§8. The Laurent polynomial extension category A^z"
§9. Nilpotent class
§10. A-theory of A^,*"
§11. Lower K-theory
§12. Transfer in X-theory
§13. Quadratic L-theory
§14. Excision and transversality in L-theory
§15. i-theory of d(A)
§16. L-theory of A^z"
§17. Lower L-theory
§18. Transfer in L-theory
§19. Symmetric L-theory
§20. The algebraic fibering obstruction
References
Index