Lower K-& L-Theory

ISBN-13: 9780521438018 / Angielski / Miękka / 1992 / 184 str.

A. A. Ranicki; Andrew Ranicki

Opis

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.

Spis treści

Introduction; 1. Projective class and torsion; 2. Graded and bounded categories; 3. End invariants; 4. Excision and transversality in K-theory; 5. Isomorphism torsion; 6. Open cones; 7. K-theory of C1 (A); 8. The Laurent polynominal extension category A[z, z-1]; 9. Nilpotent class; 10. K-theory of A[z, z-1]; 11. Lower K-theory; 12. Transfer in K-theory; 13. Quadratic L-theory; 14. Excision and transversality in L-theory; 15. L-theory of C1 (A); 16. L-theory of A[z, z-1]; 17. Lower L-theory; 18. Transfer in L-theory; 19. Symmetric L-theory; 20. The algebraic fibering obstruction; References; Index.