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  1. Complete list of research papers by C.T.C. Wall
  2. 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.

Søren Galatius 1.1, Cobordisms (IAS - PCMI)

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.

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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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