# Questions about surgery theory

From Manifold Atlas

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 do I tell if a space is homotopy equivalent to a manifold?

This is in fact a Mathoverflow question.

### 1.2 Simply connected odd-dimensional L-groups

How does one prove that ?

Read [Kervaire&Milnor1963, Section 6] and/or [Browder1972, IV.3] and/or [Ranicki2002, 12.6].

## 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