Category:Surgery

Revision as of 17:37, 17 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".

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.

Suggestions for pages on MAP

There are already many Wikipedia pages on surgery: MAP aims for more in-depth pages.

I) List of prerequisites: Quadratic forms for surgery, Bordism, Transversality, Characteristic classes, Homotopy and Homology, Immersions, Embeddings, Signature theorem, h-cobordism theorem, Whitehead torsion, Generalised Poincaré conjecture

II) Main articles: The structure set, Surgery classification of manifolds, Poincaré complexes, Surgery exact sequence, Normal maps, Surgery obstruction groups, L-Theory, Tables of computations of L-groups, Assembly maps, Bounded and controlled topology.

III) Fields of application: Classification of high-dimensional manifolds, Topological manifolds, Farrell-Jones Conjecture, Borel-Conjecture, Novikov-Conjecture, Operator algebras, Group actions, Stratified sets, Scalar curvature, Automorphisms of manifolds, Fake tori.