Category:Surgery

Revision as of 11:34, 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".

1 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

2 Existing Wikipedia pages

2.1 Pages specific to surgery

• Arf invariant
• Baum-Connes conjecture
• Borel conjecture
• Categories of manifolds
• Characteristic classes
• Classification of manifolds
• Cobordism
• Differential manifold
• Differential structure
• Differential topology
• Embedding
• ε-quadratic form
• Exotic sphere
• Farrell-Jones Conjecture
• Handlebody
• Hauptvermutung
• h-cobordism also s-cobordism
• Hirzebruch signature theorem
• Homotopy Groups of Spheres
• Immersion
• Index theory
• Intersection theory
• Kervaire invariant
• Kirby Siebenmann obstruction
• Lens space
• L-theory
• Manifold
• Morse theory
• Normal bundle
• Novikov conjecture
• Poincare conjecture
• Poincare duality
• Pontrjagin class
• Quadratic form
• Regular homotopy
• Rokhlin's theorem
• Signature (topology)
• Surgery Theory
• Transversality
• Whitehead torsion

2.2 Pages on related topics

• Algebraic K-theory
• Fundamental Group
• Homology and cohomology
• Homotopy
• Homotopy Group
• List of conjectures (not just in surgery theory)
• Reidemeister torsion