Date

Page

Correction

11.11.2020


added missing reference to Lee's book on smooth manifolds

11.11.2020

p. 22

Definition 1.2.1: last part of the defintition: changed x to y.

12.11.2020

p. 22

diagram: corrected label of left vertical arrow

19.11.2020

p. 40

Corollary 1.3.7: added missing condition (dim M is nonzero)

19.11.2020

p. 42/43

Example 1.3.15: corrected the definition of the warped product

26.11.2020

p. 41

Example 1.3.9: longer > shorter

26.11.2020

p. 48

Proposition 1.4.7: Added connectedness assumption.

26.11.2020

p. 49

line 2: introduced x^1, ..., x^n

26.11.2020

p. 49

Proposition 1.4.10: \S^0 is not connected (thus not symmetric)

26.11.2020

p. 50

proof of Proposition 1.4.10: corrected definition of N

03.12.2020

p. 64

Example 1.4.25: radius corrected

03.12.2020

p. 63

Example 1.5.4: typos corrected

03.12.2020

p. 67

Corollary 1.5.12: added the claim that the closure of V is contained in U
(this is satisfied by construction and improves applicability of the statement).

03.12.2020

Week 6

Exercise 5.2: corrected the definition of the action for the Klein bottle

04.12.2020

p. 74

Proposition 1.5.27: added missing det

09.12.2020

p. 71

Remark 1.5.14: corrected the integration formulae (missing inverse of the chart)

10.12.2020

p. 85/86

Remark 2.1.12: corrected two typos in the formulae (missing ^U and missing sum)

11.12.2020

p. 94

Definition 2.2.31: removed confusing condition "s < t".

17.12.2020

p. 93

Remark 2.2.28: corrected indices in the parallel transport equation

21.12.2020

Week 8.5

curves: cleaned up the first sentence

23.12.2020

p. 87

Figure 2.2: Adobe Reader couldn't handle this; this should be fixed now.

07.01.2021

p. 83

Example 2.2.8: Vector fields cannot necessarily be extended to all of \R^N
if M is not closed. The statements are corrected accordingly.

07.01.2021

p. 106

ungarbled the computation in the proof of part 3.

08.01.2021

Week 9

Exercise 8.2: Added missing parentheses in the definition of T

13.01.2021

p. 111

Definition 2.4.4: corrected target type of Rm

13.01.2021

p. 111

Remark 2.4.5: small clarification

13.01.2021

p. 112f

Proposition 2.4.7: M_1 instead of M; added missing composition with phi.

13.01.2021

p. 114

proof of 2.: typo

18.01.2021

p. 138141

corrected several of the differentiation indices

20.01.2021


corrected several typos; mainly concerning Chapter 2.5 and 3.1.1

21.01.2021

p. 136

Proposition 3.1.14: added condition to uniformly normal neighbourhoods (as in the lecture)

21.01.2021

p. 140

proof of Proposition 3.2.7: the proof starts now with choosing a Riemannian metric on M

24.01.2021

p. 124

Theorem 2.5.5; formula in part (1): the last part is corrected.

31.01.2021

Week 12

Exercise 11.3: Corrected/clarified hypothesis on the curve gamma.

31.01.2021

p. 159

Remark 3.5.1: Corrected/clarified hypothesis on the curve gamma.

03.02.2021

Week 12

Exercise 11.4: "symmetric" instead of "locally symmetric";
as this is on very short notice: If you already worked on this problem and showed that the
previous formulation was incorrect, then this is also fine!

04.02.2021

p. 169

proof of Theorem 3.5.15: added missing signs

04.02.2021

p. 164

proof of Proposition 3.5.7: corrected the blunder (as discussed in the lecture)

10.02.2021

p. 178

typos in the proof of Theorem 4.3.2 corrected



