HIGH-DIMENSIONAL KNOT THEORY: ALGEBRAIC SURGERY IN CODIMENSION
TABLE OF CONTENTS PART ONE ALGEBRAIC K-THEORY 1 FINITE STRUCTURES 1A THE WALL ?NITENESS OBSTRUCTION 1B WHITEHEAD TORSION 1C THE MAPPING TORUS 2 GEOMETRIC BANDS 3 ALGEBRAIC BANDS LOCALIZATION AND COMPLETION IN K-THEORY 4A COMMUTATIVE LOCALIZATION 4B THE ALGEBRAIC K-THEORY LOCALIZATION EXACT SEQUENCE 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 10A THE ENDOMORPHISM CATEGORY + A[Z] 10C THE A-CONTRACTIBLE LOCALIZATION ??1A[Z, Z?1] 11 THE CHARACTERISTIC POLYNOMIAL 12 PRIMARY K-THEORY 13 AUTOMORPHISM K-THEORY 13A THE FREDHOLM LOCALIZATION ??1A[Z, Z?1] 13B THE AUTOMORPHISM CATEGORY 14 WITT VECTORS 15 THE ?BERING OBSTRUCTION 16 REIDEMEISTER TORSION 17 ALEXANDER POLYNOMIALS 18 K-THEORY OF DEDEKIND RINGS 19 K-THEORY OF FUNCTION ?ELDS PART TWO ALGEBRAIC L-THEORY 20 ALGEBRAIC POINCAR´E COMPLEXES 20A L-GROUPS 20B ?-GROUPS 20C THICKENINGS, UNIONS AND TRIADS 21 CODIMENSION Q SURGERY 21A SURGERY ON SUBMANIFOLDS 21B THE SPLITTING OBSTRUCTION 22 CODIMENSION 2 SURGERY 22A CHARACTERISTIC SUBMANIFOLDS 22B THE ANTIQUADRATIC CONSTRUCTION 22C SPINES 22D THE HOMOLOGY SPLITTING OBSTRUCTION 24 L-THEORY OF LAURENT EXTENSIONS 25 LOCALIZATION AND COMPLETION IN L-THEORY 26 ASYMMETRIC L-THEORY 27 FRAMED CODIMENSION 2 SURGERY 27A CODIMENSION 1 SEIFERT SURFACES 27B CODIMENSION 2 SEIFERT SURFACES 27C BRANCHED CYCLIC COVERS 27D FRAMED SPINES 28 AUTOMORPHISM L-THEORY 28A ALGEBRAIC POINCAR´E BANDS 28B DUALITY IN AUTOMORPHISM K-THEORY 28C BORDISM OF AUTOMORPHISMS OF MANIFOLDS 28D THE AUTOMORPHISM SIGNATURE 28E THE TRACE MAP ?Z 28F AUTOMORPHISM AND ASYMMETRIC L-THEORY 29 OPEN BOOKS 29A GEOMETRIC OPEN BOOKS 29B THE ASYMMETRIC SIGNATURE 30 TWISTED DOUBLES 30A GEOMETRIC TWISTED DOUBLES 30B ALGEBRAIC TWISTED DOUBLES 30C ALGEBRAIC OPEN BOOKS 30D TWISTED DOUBLE L-THEORY 31 ISOMETRIC L-THEORY 31A ISOMETRIC STRUCTURES 31B THE TRACE MAP ?S 32 SEIFERT AND BLANCH?ELD COMPLEXES 32A SEIFERT COMPLEXES 32B BLANCH?ELD COMPLEXES 32C FIBRED SEIFERT AND BLANCH?ELD COMPLEXES 32D BASED SEIFERT AND BLANCH?ELD COMPLEXES 32E MINIMAL SEIFERT COMPLEXES 33 KNOT THEORY 33A THE SEIFERT COMPLEX OF AN N-KNOT 33B FIBRED KNOTS 33C THE BLANCH?ELD COMPLEX OF AN N-KNOT 33D SIMPLE KNOTS 33E THE ALEXANDER POLYNOMIALS OF AN N-KNOT 34 ENDOMORPHISM L-THEORY 34A ENDOMETRIC STRUCTURES 34B THE TRACE MAP ?X 35 PRIMARY L-THEORY 35A ENDOMORPHISM L-THEORY 35B ISOMETRIC L-THEORY 35C AUTOMORPHISM L-THEORY 35D ASYMMETRIC L-THEORY 36 ALMOST SYMMETRIC L-THEORY 37 L-THEORY OF ?ELDS AND RATIONAL LOCALIZATION 37A FIELDS 37B RATIONAL LOCALIZATION 38 L-THEORY OF DEDEKIND RINGS 39 L-THEORY OF FUNCTION ?ELDS 39A L-THEORY OF F(X) (X = X) 39B L-THEORY OF F(S) (S = 1 ?S) 39C L-THEORY OF F(Z) (Z = Z?1) 39D THE ASYMMETRIC L-THEORY OF F 39E THE AUTOMORPHISM L-THEORY OF F 40 THE MULTISIGNATURE 40A ISOMETRIC MULTISIGNATURE 40B ASYMMETRIC MULTISIGNATURE 40C THE ?-SIGNATURES 40D AUTOMORPHISM MULTISIGNATURE 41 COUPLING INVARIANTS 41A ENDOMORPHISM L-THEORY 41B ISOMETRIC L-THEORY 41C AUTOMORPHISM L-THEORY 42 THE KNOT COBORDISM GROUPS