# Surgery

From Encyclopedia of Mathematics

*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 for details.

#### Comments

Cf. also Morse surgery.

**How to Cite This Entry:**

Surgery.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Surgery&oldid=32442

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article