# LMS: 178 Lower K- and L- Theory (London Mathematical Society Lecture Note Series)

Cambridge University Press, 8/21/2008

EAN 9780521438018, ISBN10: 0521438012

Paperback, 184 pages, 22.9 x 15.2 x 1.1 cm

Language: English

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.

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.