Category:Surgery

Revision as of 11:54, 6 August 2010

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".

Plans for pages on MAP

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

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