- Complete list of research papers by C.T.C. Wall
- IMSc Library catalog › Details for: Bordism of diffeomorphisms and related topics
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Dec , Mapping class groups of highly connected manifolds , Workshop "Manifolds" during the programme "Homotopy harnessing higher structures", Newton Institute Cambridge. Nov , Detecting exotic smooth structures in diffeomorphism groups , Differential Geometry and Topology Seminar, Cambridge.
Apr , Detecting exotic smooth structures in diffeomorphism groups , Topology Seminar, Northwestern. Jan , On characteristic classes of exotic manifold bundles , Topology Seminar, Karlsruhe.
Complete list of research papers by C.T.C. Wall
Dec , On characteristic classes of exotic manifold bundles , Topology Seminar, Copenhagen. July , On the cohomology of moduli spaces of manifolds connect summed with an exotic sphere , Young Topologists' Meeting, Stockholm. Contact Information Address:.
Farb and Margulit, A primer on mapping class groups, pg Here is how you prove surjectivity; this amounts to proving that an invertible cobordism is a product respecting all identifications. I am ignoring the actual identification maps you need to keep track of things in your category, but the argument would work as stated with more notation and care.
IMSc Library catalog › Details for: Bordism of diffeomorphisms and related topics
Then I claim that both A and B are product cobordisms. By the Hopfian property of surface groups, it is an isomorphism. The same argument applies to the maps induced by including F into B. The Univ.
I believe that the proof of Stallings' theorem would actually give you a product respecting all identifications so that the resulting isotopy induces the given automorphism. You can also get this by Waldhausen's general theory of Haken manifolds On irreducible 3-manifolds which are sufficiently large.
Either proof of the product theorem would essentially proceed by finding a hierarchy for A and B that looks like you took a system of curves and arcs cutting F into a disk, and crossed with I. This and irreducibility would imply that the intersection of the cylinders and disks cuts each of A and B up into a ball, from which you get the product structure using Alexander's theorem. Sign up to join this community.
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https://liptiotulo.tk The keyword is Morse theory. This is the first thing varying conditions like compactness one proves in this direction. A standard and good reference is Milnor's aptly named Morse theory.
Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. A problem about diffeomorphism of two components of the boundary of a manifold.
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