Wiki source code of Homotopy theory, fall 2015

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1 = Homotopy theory, fall 2015 =
2
3
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5 {{panel}}
6 **Teacher:** [[Erik Elfving>>doc:mathstatHenkilokunta.Elfving, Erik]]
7
8 **Scope:** 10 cr
9
10 **Type:** Advanced studies
11
12 **Teaching: Lectures and exercises
13 **
14
15 **Topics: Fundamental group, applications, covering spaces, higher homotopy groups, fibrations and cofibrations
16 **
17
18 **Prerequisites: Topology II, a first course in abstract algebra
19 **
20 {{/panel}}
21
22 === {{toc maxLevel="4" minLevel="2" indent="20px"/}} ===
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24 (% class="confluence-link" %)
25 == News ==
26
27 * The course starts on Wednesday, 2nd of September (no lecture on Monday 31st of August). On Thursday, 3rd of September, there will be an extra lecture (12-14, B321).
28
29 == Teaching schedule ==
30
31 Weeks 36-42 and 44-50, Monday 10-12 and Wednesday 14-16 in room C124. In addition, two hours of exercise classes per week. Guidance in Ratkomo (3rd floor corridor) on Wednesdays 10-12.
32
33 == Exams ==
34
35 One exam at the end of the course, on Monday 21st of December, 10-14, auditorium A111.
36
37 == Course material ==
38
39 Lecture notes (in Finnish):[[attach:htteoria.pdf]]
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41 Liite:[[attach:Parakompaktisuus.pdf]]
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43 Metsänkylä-Näätänen: Algebra, p. 92-98:[[attach:D4.pdf]]
44
45 In English: W. S. Massey: Algebraic topology: an introduction; A. Hatcher: Algebraic topology; E. H. Spanier: Algebraic topology
46
47 Preliminary schedule:
48
49 1. Homotopy of mappings; path homotopy; fundamental group; covering map; the fundamental group of a circle; examples.
50 1. Applications: Brouwer's fixed point theorem and Borsuk-Ulam theorem (in dimension 2); fundamental theorem of algebra.
51 1. More about covering spaces; monodromy theorems; connection with the fundamental group; classification of covering maps; universal covering space.
52 1. Higher homotopy groups; examples of homotopy groups of spheres; the Hopf mapping S^3 -> S^2; Freudenthal suspension.
53 1. Relative homotopy groups; exact homotopy sequences.
54
55 == [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57072||shape="rect"]] ==
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57
58 (% style="color: rgb(96,96,96);" %)Did you forget to register? (%%)[[What to do?>>url:https://wiki.helsinki.fi/display/mathstatOpiskelu/Kysymys4||style="text-decoration: underline;" shape="rect"]]
59
60 == Exercises ==
61
62 === Assignments ===
63
64 * Exercise 1 (10.9.2015): [[attach:h1t.pdf]],[[attach:h1r.pdf]]
65 * Exercise 2 (17.9.2015): [[h2t.pdf,>>attach:h2t.pdf]][[attach:h2r.pdf]]
66 * Exercise 3 (24.9.2015): [[attach:h3t.pdf]],[[attach:h3r.pdf]]
67 * Exercise 4 (1.10.2015): [[attach:h4t.pdf]],[[attach:h4r.pdf]]
68 * Exercise 5 (8.10.2015): [[attach:h5t.pdf]],[[attach:h5r.pdf]]
69 * Exercise 6 (15.10.2015): [[h6t.pdf,>>attach:h6t.pdf]][[attach:h6r.pdf]]
70 * Exercise 7 (29.10.2015): [[attach:h7t.pdf]],[[attach:h7r.pdf]]
71 * Exercise 8 (5.11.2015): [[attach:h8t.pdf]],[[attach:h8r.pdf]]
72 * Exercise 9 (12.11.2015): [[attach:h9t.pdf]],[[attach:h9r.pdf]]
73 * Exercise 10 (19.11.2015): [[attach:h10t.pdf]],[[attach:h10r.pdf]]
74 * Exercise 11 (26.11.2015): [[attach:h11t.pdf]],[[attach:h11r.pdf]]
75 * Exercise 12 (3.12.2015): [[attach:h12t.pdf]],[[attach:h12r.pdf]]
76 * Exercise 13 (10.12.2015): [[attach:h13t.pdf]],[[attach:h13r.pdf]]
77
78 === Exercise classes ===
79
80 |=(((
81 Group
82 )))|=(((
83 Day
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85 Time
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87 Room
88 )))|=(% colspan="1" %)(((
89 Instructor
90 )))
91 |(((
92 1.
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94 Thursday
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96 12-14
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98 B321
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100 Erik Elfving
101 )))
102
103 == Course feedback ==
104
105 Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]].