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Every orientable 3-manifold can be obtained from the 3-sphere by doing surgery along a framed link. Kirby's theorem says that the surgery along two framed links gives homeomorphic manifolds if and ...

A celebrated theorem of Rohlin states the following An oriented closed 4-manifold $M^4$ bounds an oriented 5-manifold if and only if the signature of $M^4$ is zero. Simple homological arguments ...

Akbulut's cork is the Mazur manifold $W$ shown in the picture below, This manifold carries an involution of it's boundary $f:\partial W\to \partial W$ that exchanges a meridian of the 0-framed curve ...