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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.
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- Date Published: May 1992
- format: Paperback
- isbn: 9780521438018
- length: 184 pages
- dimensions: 229 x 152 x 11 mm
- weight: 0.28kg
- availability: Available
Table of Contents
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
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