Applied Algebraic Topology, WS 2022/23

Correction log for the lecture notes:

Date	Page	Correction
08.11.2022	p. 33	Definition 2.3.28: p_2(\sigma) \in Y (instead of p_1(\sigma) \in Y)
08.11.2022	p. 30	Example 2.3.17: y \in V(Y) (instead of y \in V(T)); similarly in Exercise 3.A
22.11.2022	Sheet 4	Exercise 4.2: X should be a simplicial complex
22.11.2022	p. 46	Proposisition 2.6.9: X should be a simplicial complex
22.11.2022	p. 56	Theorem 2.6.26: cleaned up the hypotheses
02.12.2022	p. 66	Remark 2.8.2: second case of union: replaced one find(y) with find(x)
10.01.2023	p. 4	Moved sensor network coverage to appropriate location
10.01.2023	p. 115	Example 3.8.4: corrected 1/2 to 1/3 in the given Nash equilibrium
13.01.2023	p. 126	Definition 4.2.1, 4.2.3: slightly improved the definitions (it is now clarified what is part of the structure)
15.01.2023	p. 126	inserted Figure 4.2 (for Example 4.1.13)
15.01.2023	p. 127	Example 4.2.2 "domain" ist not needed; clarified the grading
15.01.2023	p. 128	Theorem 4.2.7: replaced "R_0 is a field" with "R \neq R_0" (the first version also leads to a true statement)
17.01.2023	p. 132	Lemma 4.2.11: reformulated the lemma in such a way that it can be applied in the existence proof (the proof of the lemma is strong enough to provide this statement).
20.01.2023	p. 125	Definition 4.1.12: adapted death/persistence of classes to the standard notions
24.01.2023	p. 138	Proposition 4.3.5: added definition of k(j)
31.01.2023	p. 135f	Example 4.2.18, 4.2.19: corrected the computations (pagebreaks changed slightly after that)
31.01.2023	p. 148	Algorithm 4.3.23: the outer loop is corrected (with respect to the lecture on 27.01.2023)
31.01.2023	Sheet 13	Exercise 1: the non-triviality condition is corrected
01.02.2023	p. 136	Definition 4.3.1: corrected typo in the degree compatibility equation
03.02.2023	p. 103	proof of Sperner's lemma: clarified the proof a bit