Inertia group II (Ex)
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Let be a closed smooth oriented -manifold. The homotopy inertia group of , , is the subgroup of homotopy -spheres defined by
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Tex syntax errorwe regard and as the same topological space (with different smooth structures).
Exercise 0.1.
- Show that if and only if
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is equivalent toTex syntax error
in . - Given that , determine .
- Assuming that , deduce that admits a self-homotopy equivalence which is not homotopic to a diffeomorphism.