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By Selman Akbulut

ISBN-10: 0198784864

ISBN-13: 9780198784869

This e-book offers the topology of gentle 4-manifolds in an intuitive self-contained approach, constructed over a couple of years by way of Professor Akbulut. The textual content is aimed toward graduate scholars and makes a speciality of the educating and studying of the topic, giving a right away method of buildings and theorems that are supplemented through routines to aid the reader paintings during the info no longer coated within the proofs.

The publication includes a hundred color illustrations to illustrate the tips instead of offering long-winded and almost certainly uncertain causes. Key effects were chosen that relate to the cloth mentioned and the writer has supplied examples of ways to examine them with the thoughts constructed in previous chapters.

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6, which is −M ⌣f N. e. creating tunnels). We don’t need to describe how f identifies the 2- and 3-handles of M with that of N, since by the similar description, they amount to adding 3- and 4- handles to −M ⊔ N. Recall that describing 4-manifold handlebodies we don’t need to specify 3- and 4-handles, because they are always attached canonically. 7, because in this case the identifying cylinder L × [0, 1] is attached to a single connected manifold M, as opposed to between two disjoint manifolds −M ⊔ N.

11. 8. To construct E ′ we simply cross this twisted F2 bundle over the circle F2 ×τ S 1 with S 1 . 9. 4. 14 describes E0′ = E ′ −F2 ×D 2 . 15. 15. 16. 17. 16 by f2−1 ○ f1 . 3 General surface bundles over surfaces Now it is clear how to proceed in drawing a handlebody picture of a general Fg bundle ˜ Fp . 18. By removing Fg × D 2 from each, we write M =⌣∂ Ej , where each Ej is a Fg bundle over T02 , then we perform gluing operations along the boundaries, as described in Chapter 3. 2 p Fg ... e.

4 20 ... 1 Plumbing For i = 1, 2 let Di ↪ Ei → Si be two Euler class ki disk bundles over the 2-spheres Si , and ≈ let Bi ⊂ Si be the disks giving the trivializations Ei ∣Bi → Bi × Di . Plumbing E1 and E2 is the process of gluing them together by identifying D1 × B1 with B2 × D2 (by switching base and fiber directions). Hence, in this manifold if we locate ourselves on the boundary of D1 × B1 = B 4 , we will see a two 2-handles attached to B 4 along the link of Hopf circles {∂D1 , ∂B1 } with framings k1 , k2 .

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4-Manifolds by Selman Akbulut


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