# 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 08:26, 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