| 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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