User everknight - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T09:44:23Z http://mathoverflow.net/feeds/user/27118 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109235/exotic-spheres-signature Exotic Spheres Signature Everknight 2012-10-09T15:07:34Z 2012-11-30T11:22:00Z <p>I'm studying the groups of homotpy spheres, which yields to the study of classes of diffeomorphism over the standard sphere. I dont understand why the examples are focused to construct manifolds with signature non-zero and boundary a homotopy sphere.</p> <p>That is, $W$ a $4n$-manifold with $\sigma(W)\neq 0$ and $\partial W \cong S^{4n-1}$ then $\partial W$ is exotic.</p> <p>Or I am just misunderstanding the invariants. Thanks</p>