Surgery resources

Revision as of 19:00, 13 September 2010

This page gives links to resources on surgery theory.

1 Weblinks

• Andrew Ranicki's surgery bits and pieces
• Misha Gromov's website

2 Bibliography

• [Milnor1961]
• [Browder1972]
• [Farrell1982] (contains a suggested redaing programme)
• [Kervaire&Milnor1963]
• [Kirby&Siebenmann1977]
• [Lück2001]
• [Ranicki2002]
• [Wall1999]

3 Wikipedia pages

3.1 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
• Structure Set
• Transversality
• Whitehead torsion

3.2 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

4 References

• [Browder1972] W. Browder, Surgery on simply-connected manifolds, Springer-Verlag, New York, 1972. MR0358813 (50 #11272) Zbl 0543.57003
• [Farrell1982] F. T. Farrell, Review of "Exact sequences in algebraic surgery by A. A. Ranicki", Mathematical Reviews MR0620795 (82h:57027)
• [Kervaire&Milnor1963] M. A. Kervaire and J. W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR0148075 (26 #5584) Zbl 0115.40505
• [Kirby&Siebenmann1977] R. C. Kirby and L. C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Princeton University Press, Princeton, N.J., 1977. MR0645390 (58 #31082) Zbl 0361.57004
• [Lück2001] W. Lück, A basic introduction to surgery theory, 9 (2001), 1–224. Available from the author's homepage. MR1937016 (2004a:57041) Zbl 1045.57020
• [Milnor1961] J. Milnor, A procedure for killing homotopy groups of differentiable manifolds, Proc. Sympos. Pure Math, Vol. III (1961), 39–55. MR0130696 (24 #A556) Zbl 0118.18601
• [Ranicki2002] A. Ranicki, Algebraic and geometric surgery, The Clarendon Press Oxford University Press, Oxford, 2002. MR2061749 (2005e:57075) Zbl 1003.57001
• [Wall1999] C. T. C. Wall, Surgery on compact manifolds, American Mathematical Society, Providence, RI, 1999. MR1687388 (2000a:57089) Zbl 0935.57003