Surgery Theory

A collection of techniques and an algebraic framework for altering and classifying manifolds by cutting out embedded spheres with tubular neighbourhoods and gluing in complementary disk bundles along specified framings; a k‑surgery on an n‑manifold replaces an embedded S^k × D^{n−k} with D^{k+1} × S^{n−k−1} to change homotopy and handle structure.