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In the first section of "A procedure for killing homotopy groups of differentiable manifolds", Milnor gives the surgery construction as follows. Let $W$ be an $n=p+q+1$ dimensional manifold. ...

Recall that a surgery of codimension $q$ on an $n$-manifold $X$ is a modification of $X$ of the following type. Let $\Sigma^{n-q}\subset X$ be a smoothly embedded $(n-q)$-sphere with a trivialized ...

I already asked this question on the Math Stack Exchange but did not get an answer. I am currently working through Geiges proof of the Martinet-Lutz theorem, which can be found here, and am trying to ...

I need to find various ways of performing two surgeries on a collection of circles so that the resulting 2-dimensional cobordism (the trace of the surgeries) is connected. How can I find these ? up ...

I am looking for an expository text on the paper "The classification of simply connected manifolds of positive scalar curvature" by Gromov and Lawson, in particular on the proof of Theorem A....