Category:Surgery

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[[Category:Manifolds]]
[[Category:Manifolds]]
== Existing Wikipedia pages ==
=== Pages specific to surgery ===
<!-- * [[Wikipedia:Arf_invariant|Arf invariant]] -->
*[http://en.wikipedia.org/wiki/Arf_invariant Arf invariant]
<!-- *[[Assembly]] -->
*[http://en.wikipedia.org/wiki/Baum%E2%80%93Connes_conjecture Baum-Connes conjecture]
*[http://en.wikipedia.org/wiki/Borel_conjecture Borel conjecture]
*[http://en.wikipedia.org/wiki/Categories_of_manifolds Categories of manifolds]
*[http://en.wikipedia.org/wiki/Characteristic_classes Characteristic classes]
*[http://en.wikipedia.org/wiki/Classification_of_manifolds Classification of manifolds]
*[http://en.wikipedia.org/wiki/Cobordism Cobordism]
*[http://en.wikipedia.org/wiki/Differentiable_manifold Differential manifold]
*[http://en.wikipedia.org/wiki/Differential_structure Differential structure]
*[http://en.wikipedia.org/wiki/Differential_topology Differential topology]
*[http://en.wikipedia.org/wiki/Embedding Embedding]
*[http://en.wikipedia.org/wiki/%CE%95-quadratic_form ε-quadratic form]
*[http://en.wikipedia.org/wiki/Exotic_sphere Exotic sphere]
*[http://en.wikipedia.org/wiki/Farrell-Jones_conjecture Farrell-Jones Conjecture]
*[http://en.wikipedia.org/wiki/Handlebody Handlebody]
*[http://en.wikipedia.org/wiki/Hauptvermutung Hauptvermutung]
*[http://en.wikipedia.org/wiki/H-cobordism h-cobordism also s-cobordism]
*[http://en.wikipedia.org/wiki/Hirzebruch_signature_theorem Hirzebruch signature theorem]
*[http://en.wikipedia.org/wiki/Homotopy_groups_of_spheres Homotopy Groups of Spheres]
*[http://en.wikipedia.org/wiki/Immersion_(mathematics) Immersion]
*[http://en.wikipedia.org/wiki/Index_theory Index theory]
*[http://en.wikipedia.org/wiki/Intersection_theory Intersection theory]
*[http://en.wikipedia.org/wiki/Kervaire_invariant Kervaire invariant]
<!-- *[[Kervaire manifold]] -->
*[http://en.wikipedia.org/wiki/Kirby-Siebenmann_obstruction Kirby Siebenmann obstruction]
*[http://en.wikipedia.org/wiki/lens_space Lens space]
*[http://en.wikipedia.org/wiki/L-theory L-theory]
*[http://en.wikipedia.org/wiki/Manifold Manifold]
<!-- *[[Milnor manifold]] -->
*[http://en.wikipedia.org/wiki/Morse_theory Morse theory]
*[http://en.wikipedia.org/wiki/Normal_bundle Normal bundle]
<!-- *[[Normal maps in surgery theory]] -->
*[http://en.wikipedia.org/wiki/Novikov_conjecture Novikov conjecture]
<!-- *[[Plumbing in topology]] -->
<!-- *[[Poincaré complexes]] -->
*[http://en.wikipedia.org/wiki/Poincare_conjecture Poincare conjecture]
*[http://en.wikipedia.org/wiki/Poincare_dual Poincare duality]
*[http://en.wikipedia.org/wiki/Pontrjagin_class Pontrjagin class]
*[http://en.wikipedia.org/wiki/Quadratic_form Quadratic form]
*[http://en.wikipedia.org/wiki/Regular_homotopy Regular homotopy]
<!--*[[Ring with involution]] -->
*[http://en.wikipedia.org/wiki/Rokhlin%27s_theorem Rokhlin's theorem]
*[http://en.wikipedia.org/wiki/Signature_(topology) Signature (topology)]
<!-- *[[Surgery exact sequence]] -->
<!-- *[[Surgery obstructions in topology]] -->
<!-- *[[Surgery structure set]] -->
*[http://en.wikipedia.org/wiki/Surgery_theory Surgery Theory]
*[http://en.wikipedia.org/wiki/Surgery_structure_set Structure Set]
*[http://en.wikipedia.org/wiki/Transversality Transversality]
*[http://en.wikipedia.org/wiki/Whitehead_torsion Whitehead torsion]
=== Pages on related topics ===
*[http://en.wikipedia.org/wiki/Algebraic_K-theory Algebraic K-theory]
*[http://en.wikipedia.org/wiki/Fundamental_group Fundamental Group]
*[http://en.wikipedia.org/wiki/Homology_(mathematics) Homology and cohomology]
*[http://en.wikipedia.org/wiki/Homotopy Homotopy]
*[http://en.wikipedia.org/wiki/Homotopy_group Homotopy Group]
*[http://en.wikipedia.org/wiki/List_of_conjectures List of conjectures] (not just in surgery theory)
*[http://en.wikipedia.org/wiki/Reidemeister_torsion Reidemeister torsion]
[[Category:Theory]]

Revision as of 11:50, 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

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