# Template:Lück2001

From Manifold Atlas

W. Lück, *A basic introduction to surgery theory*, **9** (2001), 1–224. Available from the author's homepage. MR1937016 (2004a:57041) Zbl 1045.57020

Comments and corrections for this work follow organised by chapter.

## Contents |

## [edit] 1 Chapter 1

## [edit] 2 Chapter 2

## [edit] 3 Chapter 3

page 57:

- In equation (3.22) one should mention that is a bundle over the product .
- Typos at the bottom: write instead of three times.
- Typo in line 11: write instead of .

page 58:

- typo in line 8 from the bottom: write : instead of : .
- In the proof of Theorem 3.26: is a CW complex, not a manifold. Why is a manifold? What is the exact definition of transversality here?

page 59:

- The word 'homomorphism' in line 3 is confusing, since the group structure on is not clear.
- Typo in line 9: write instead of .
- Typo in the definition of : write instead of .

page 60:

- Typo in line 3: write instead of .

page 61:

- Typo in line 1: write : instead of : .
- Typo in line 1: write : instead of : .

page 62:

- Typo in the assertion of Theorem 3.38: write instead of .

page 64:

- Typo in Lemma 3.40: write : instead of : .
- Lemma 3.40 uses the notion of degree for maps between arbitrary Poincare complexes. It would be helpful to provide a general definition of degree in the lecture notes before this lemma.

page 65:

- Typo in line 3: write instead of .
- In the three lines after 'One can arrange that these stabilization maps...' it would be useful to have a more precise explanation, why one should use cofibrations.
- Typo in line 13 from the bottom: write Spivak normal -fibration instead of Spivak normal -bundle.
- Remark 3.44: is used here but the definition of is after the Remark. It is better to give the definition of already here. Also it does not become clear what is.

page 67:

- In Definition 3.46: If two vector bundles and are isomorphic but not equal, the corresponding normal -maps should nevertheless be identified. However in this definition only equal vector bundles are identified. See Part 1 on the following discussion page for some suggestions on this definition.
- After Definition 3.46 the notion of degree of a map between Poincare pairs is used. It would be helpful to provide a general definition in the lecture notes before.
- One would like to have more details of the proof of Theorem 3.48. This theorem is an important step and thus should be treated more precisely.

page 68:

- In Definition 3.50 one should consider closed manifolds, not closed oriented manifolds. Also there are some typos in the definition of bordism after Definition 3.50. See Part 2 on the following discussion page for some suggestions on this definition.

page 69:

- In line 3 one should consider closed manifolds, not closed oriented manifolds.

## [edit] 4 Chapter 4

Example 4.20: the surgery is performed on the zero element in not in .