| Description |
1 online resource (xii, 262 pages) : illustrations (some color |
| Series |
Oxford graduate texts in mathematics ;; 25 |
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Oxford graduate texts in mathematics ;; 25.
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| Contents |
Cover;; Preface;; Contents;; Chapter 1 4-manifold handlebodies;; 1.1 Carving (invariant notation of 1-handle);; 1.2 Sliding handles;; 1.3 Canceling handles;; 1.4 Carving ribbons;; 1.5 Non-orientable handles;; 1.6 Algebraic topology;; Chapter 2 Building low-dimensional manifolds;; 2.1 Plumbing;; 2.2 Self plumbing;; 2.3 Some useful diffeomorphisms;; 2.4 Examples;; 2.5 Constructing diffeomorphisms by carving;; 2.6 Shake slice knots;; 2.7 Some classical invariants;; Chapter 3 Gluing 4-manifolds along their boundaries;; 3.1 Constructing −M ͜ f N by the upside down method |
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3.2 Constructing −M ͜ f N and M(f) by the cylinder method (roping)3.3 Codimension zero surgery M ↦ M′;; Chapter 4 Bundles;; 4.1 T4 = T2 × T2;; 4.2 Cacime surface;; 4.3 General surface bundles over surfaces;; 4.4 Circle bundles over 3-manifolds;; 4.5 3-manifold bundles over the circle;; Chapter 5 3-manifolds;; 5.1 Dehn surgery;; 5.2 From framed links to Heegaard diagrams;; 5.3 Gluing knot complements;; 5.4 Carving 3-manifolds;; 5.5 Rohlin invariant;; Chapter 6 Operations;; 6.1 Gluck twisting;; 6.2 Blowing down ribbons;; 6.3 Logarithmic transform;; 6.4 Luttinger surgery;; 6.5 Knot surgery |
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6.6 Rational blowdownsChapter 7 Lefschetz fibrations;; 7.1 Elliptic surface E(n);; 7.2 Dolgachev surfaces;; 7.3 PALFs;; 7.4 ALFs;; 7.5 BLFs;; Chapter 8 Symplectic manifolds;; 8.1 Contact manifolds;; 8.2 Stein manifolds;; 8.3 Eliashberg's characterization of Stein;; 8.4 Convex decomposition of 4-manifolds;; 8.5 M4 = ∣BLF∣;; 8.6 Stein = ∣PALF∣;; 8.7 Imbedding Stein to symplectic via PALF;; 8.8 Symplectic fillings;; Chapter 9 Exotic 4-manifolds;; 9.1 Constructing small exotic manifolds;; 9.2 Iterated 0-Whitehead doubles are non-slice;; 9.3 A solution of a conjecture of Zeeman;; 9.4 An exotic R4 |
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13.5 Seiberg-Witten invariants13.6 S-W when b+2 (X) = 1 ;; 13.7 Blowup formula;; 13.8 S-W for torus surgeries;; 13.9 S-W for manifolds with T3 boundary ;; 13.10 S-W for logarithmic transforms;; 13.11 S-W for knot surgery XK ;; 13.12 S-W for S1 × Y 3 ;; 13.13 Moduli space near the reducible solution;; 13.14 Almost complex and symplectic structures;; 13.15 Antiholomorphic quotients;; 13.16 S-W equations on R × Y 3 ;; 13.17 Adjunction inequality;; Chapter 14 Some applications;; 14.1 10/8 theorem;; 14.2 Cappell-Shaneson homotopy spheres;; 14.3 Flexible contractible 4-manifolds |
| Summary |
In '4-Manifolds', topology and invariants of smooth 4-manifolds are presented in a self-contained way. In particular handlebodies of 4-manifolds, symplectic and stein structures and Seiberg-Witten invariants are discussed |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Four-manifolds (Topology)
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MATHEMATICS -- Topology.
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Four-manifolds (Topology)
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| Form |
Electronic book
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| ISBN |
9780191827136 |
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0191827134 |
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0191087750 |
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9780191087752 |
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