Category:Surgery

This Category contains pages about surgery theory and the surgery classification of manifolds: it is the "home page" of the "surgery project".

Andrew Ranicki is the organiser of the "surgery project".

Please email Andrew if you wish to contribute to one of the projected articles, or if you have a suggestion for an article on a particular topic, or with any other suggestion of matter to be included.

Plans for pages on MAP

I) List of prerequisites: Quadratic forms for surgery, Bordism, transversality, characteristic classes, homotopy & homology, immersions & embeddings, signature theorem, h-cobordism theorem, Whitehead torsion, Generalised Poincaré conjecture

II) Main article: Structure set, surgery classification of manifolds, Poincaré complexes, surgery exact sequence, L-theory, normal maps, "updating Wall's book", tables of computations of L-groups, surgery obstructions, assembly maps, surgery theory

III) Fields of application: Classification of high-dimensional manifolds, Farrell-Jones Conjecture, Borel-Conjecture, Novikov-Conjecture, operator algebras, pure algebra (quadratic forms), group actions, stratified sets, scalar curvature (differential geometry), index theorems, automorphisms of manifolds