Lower K-& L-Theory
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This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author. These groups arise as the Grothendieck groups of modules and quadratic forms which are components of the K- and L-groups of polynomial extensions. They are important in the topology of non-compact manifolds such as Euclidean spaces, being the value groups for Whitehead torsion, the Siebemann end obstruction and the Wall finiteness and surgery obstructions. Some of the applications to topology are included, such as the obstruction theories for splitting homotopy equivalences and ...
This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author. These groups arise as the Grothendieck groups of modules and quadratic forms which are components of the K- and L-groups of polynomial extensions. They are important in the topology of non-compact manifolds such as Euclidean spaces, being the value groups for Whitehead torsion, the Siebemann end obstruction and the Wall finiteness and surgery obstructions. Some of the applications to topology are included, such as the obstruction theories for splitting homotopy equivalences and for fibering compact manifolds over the circle. Only elementary algebraic constructions are used, which are always motivated by topology. The material is accessible to a wide mathematical audience, especially graduate students and research workers in topology and algebra.
Table of contents:
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.
Table of contents:
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.