Read e-book online 4-Manifolds PDF

By Selman Akbulut

ISBN-10: 0198784864

ISBN-13: 9780198784869

This e-book offers the topology of tender 4-manifolds in an intuitive self-contained approach, built over a few years by way of Professor Akbulut. The textual content is geared toward graduate scholars and makes a speciality of the instructing and studying of the topic, giving an instantaneous method of buildings and theorems that are supplemented by way of routines to aid the reader paintings throughout the info no longer coated within the proofs.

The publication incorporates a hundred color illustrations to illustrate the information instead of supplying long-winded and in all probability uncertain causes. Key effects were chosen that relate to the fabric mentioned and the writer has supplied examples of the way to examine them with the recommendations built in prior chapters.

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Extra resources for 4-Manifolds

Example text

2. 4). 2 Constructing −M ⌣f N and M (f ) by the cylinder method (roping) For this we attach a cylinder ∂M × [0, 1] to disjoint union −M ⊔ N, where one end of the cylinder is attached by the identity, the other end is attached by the diffeomorphism f ∶ ∂M → ∂N. 2 Constructing −M ⌣f N and M(f ) by the cylinder method (roping) Think of f as a force field hovering over −M ⊔ N carrying points of ∂M to ∂N. 5. 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.

2. 4). 2 Constructing −M ⌣f N and M (f ) by the cylinder method (roping) For this we attach a cylinder ∂M × [0, 1] to disjoint union −M ⊔ N, where one end of the cylinder is attached by the identity, the other end is attached by the diffeomorphism f ∶ ∂M → ∂N. 2 Constructing −M ⌣f N and M(f ) by the cylinder method (roping) Think of f as a force field hovering over −M ⊔ N carrying points of ∂M to ∂N. 5. 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.

21). The second one is the normal bundle of an imbedding RP2 ⊂ R4 . 5 Constructing diffeomorphisms by carving ≈ Given a diffeomorphism f ∶ ∂M → ∂N, when does f extend to a diffeomorphism inside F ∶ M → N? Some instances of carving can provide a solution. One necessary condition is that f must extend to a homotopy equivalence inside, so let us assume this as a hypothesis. Now let us start with M = MΛ , where Λ = {K1rn , . . , Knrn , C1 , . . , Cs }, and let {γ1 , . . e. γj = ∂Bj , where Bj is the co-core r of the dual 2-handle of Kj j .

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4-Manifolds by Selman Akbulut


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