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Lower K- and L-theory : London Mathematical Society Lecture Note Series - Andrew Ranicki

Lower K- and L-theory

London Mathematical Society Lecture Note Series


Published: 20th July 1992
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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 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.

Projective class and torsion
Graded and bounded categories
End invariants
Excision and transversality in K-theory
Isomorphism torsion
Open cones
K-theory of C1 (A)
The Laurent polynominal extension category A[z, z-1]
Nilpotent class
K-theory of A[z, z-1]
Lower K-theory
Transfer in K-theory
Quadratic L-theory
Excision and transversality in L-theory
L-theory of C1 (A)
L-theory of A[z, z-1]
Lower L-theory
Transfer in L-theory
Symmetric L-theory
The algebraic fibering obstruction
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521438018
ISBN-10: 0521438012
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 184
Published: 20th July 1992
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.1
Weight (kg): 0.28