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''spherical surgery, on a manifold of type $(\lambda,n-\lambda)$''

A transition from one $(n-1)$-dimensional manifold $M_1$ to another manifold $M_2$, consisting in deleting a sphere of dimension $\lambda-1$ imbedded in $M_1$ and replacing it by an imbedded sphere of dimension $n-\lambda-1$. See [[Handle theory|Handle theory]] for details.



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Cf. also [[Morse surgery|Morse surgery]].