Lower K- and L-theory / Andrew Ranicki.

Format:

Book

Author/Creator:

Ranicki, Andrew, 1948- author.

Series:

London Mathematical Society lecture note series ; 178.

London Mathematical Society lecture note series ; 178

Language:

English

Subjects (All):

K-theory.

Physical Description:

1 online resource (174 pages) : digital, PDF file(s).

Other Title:

Lower K- & L-theory

L-theory.

Place of Publication:

Cambridge : Cambridge University Press, 1992.

Language Note:

English

Summary:

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.

Contents:

Cover; Title; Copyright; Dedication; 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-theoryof C1(A); 8. The Laurent polynomial 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-theory20. The algebraic fibering obstruction; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 167-171) and index.

ISBN:

1-139-88484-0

1-107-36681-X

1-107-37148-1

1-107-36190-7

0-511-96442-0

1-299-40455-3

1-107-36435-3

0-511-52632-6