Questions about surgery theory
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This is in fact a [http://mathoverflow.net/questions/129/how-can-you-tell-if-a-space-is-homotopy-equivalent-to-a-manifold Mathoverflow question]. | This is in fact a [http://mathoverflow.net/questions/129/how-can-you-tell-if-a-space-is-homotopy-equivalent-to-a-manifold Mathoverflow question]. | ||
| − | === Simply connected | + | === Simply connected surgery obstruction groups === |
<wikitex>; | <wikitex>; | ||
| − | How does one prove that $L_{2k+1}(e) = 0$ ? | + | How does one prove that |
| + | $L_{4j}(e)=Z$, $L_{4j+2}(e)=Z_2$, $L_{2k+1}(e) = 0$ ? | ||
| − | Read {{cite|Kervaire&Milnor1963 | + | Read {{cite|Kervaire&Milnor1963}} and/or {{cite|Browder1972}} and/or {{cite|Ranicki2002|Chapter 12}}. |
</wikitex> | </wikitex> | ||
Revision as of 09:26, 11 August 2010
This page organizes questions and answers about surgery theory.
The natural first port of call for quick answers is Mathoverflow.
Below is a list of questions, possibly with answers.
The Atlas also has a chapter Questions for questions which attract longer answers.
Contents |
1 Questions
1.1 How can you tell if a space is homotopy equivalent to a manifold?
This is in fact a Mathoverflow question.
1.2 Simply connected surgery obstruction groups
How does one prove that
, 
, 
?
Read [Kervaire&Milnor1963] and/or [Browder1972] and/or [Ranicki2002, Chapter 12].
2 References
- [Browder1972] W. Browder, Surgery on simply-connected manifolds, Springer-Verlag, New York, 1972. MR0358813 (50 #11272) Zbl 0543.57003
- [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
- [Ranicki2002] A. Ranicki, Algebraic and geometric surgery, The Clarendon Press Oxford University Press, Oxford, 2002. MR2061749 (2005e:57075) Zbl 1003.57001
