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High Dimensional Knot Theory

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High Dimensional Knot Theory
Algebraic surgery in codimension 2
Andrew Ranicki

Table of Contents

Part One Algebraic K-theory

1. Finite structures

2. Geometric bands

3. Algebraic bands

4. Localization and completion in K-theory

5. K-theory of polynomial extensions

6. K-theory of formal power series

7. Algebraic transversality

8. Finite domination and Novikov homology

9. Noncommutative localization

10. Endomorphism K-theory

11. The characteristic polynomial

12. Primary K-theory

13. Automorphism K-theory

14. Witt vectors

15. The fibering obstruction

16. Reidemeister torsion

17. Alexander polynomials

18. K-theory of Dedekind rings

19. K-theory of function fields

Part Two Algebraic L-theory

20. Algebraic Poincar ́ complexes

21. Codimension q surgery

22. Codimension 2 surgery

23. Manifold and geometric Poincar ́ bordism of X × S 1

24. L-theory of Laurent extensions

25. Localization and completion in L-theory

26. Asymmetric L-theory

27. Framed codimension 2 surgery

28. Automorphism L-theory

29. Open books

30. Twisted doubles

31. Isometric L-theory

32. Seifert and Blanchfield complexes

33. Knot theory

34. Endomorphism L-theory

35. Primary L-theory

36. Almost symmetric L-theory

37. L-theory of fields and rational localization

38. L-theory of Dedekind rings

39. L-theory of function fields

40. The multisignature

41. Coupling invariants

42. The knot cobordism groups

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