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1 = Introduction to algebraic topology, fall 2011 =
2
3 === Lecturer ===
4
5 Aleksandr Pasharin
6
7 === Scope ===
8
9 10 cu.
10
11 === Type ===
12
13 Advanced studies
14
15 === Prerequisites ===
16
17 Topology II, Algebra I, Linear Algebra I.
18
19 === Contents ===
20
21 The course is intended to be the first introduction to the singular homology theory and homological methods in algebraic topology.
22
23 We start off with the brief excursion to the world of simplices, simplicial methods and Delta-complexes. Then we move on to the main subject of the course - construction of the singular homology theory. We go through all the essential properties of the singular homology and apply it to prove the classical topological results such as the Invariance of Domain, Brouwer's fixed-point theorem, Brouwer-Jordan separation theorem, the main theorem of Algrebra and others.
24
25 === Lecture Notes ===
26
27 [[Foreword >>attach:01 - Foreword.pdf]]
28 [[01 - Simplicial stuff >>attach:01 - Simplicial stuff.pdf]]
29 [[02 - Homological algebra>>attach:homoalg.pdf]]
30 [[03 - Singular Homology>>attach:03 - Singular Homology.pdf]]
31 [[04 - CW complexes and cellular homology>>attach:CW-complexes.pdf]]
32
33 === Exercises ===
34
35 [[Exercises 1>>attach:01 exercise.pdf]] [[Solutions 1 >>attach:01 exercise solutions.pdf]]
36 [[Exercises 2 >>attach:02 exercise.pdf]][[Solutions 2 >>attach:02 exercise solutions.pdf]]
37 [[Exercises 3 >>attach:03 exercise.pdf]][[Solutions 3 >>attach:03 exercise solutions.pdf]]
38 [[Exercises 4 >>attach:04 exercise.pdf]][[Solutions 4 >>attach:04 exercise solutions.pdf]]
39 [[Exercises 5 >>attach:05 exercise.pdf]][[Solutions 5 >>attach:05 exercise solutions.pdf]]
40 [[Exercises 6 >>attach:06 exercise.pdf]][[Solutions 6 >>attach:06 exercise solutions.pdf]]
41 [[Exercises 7 >>attach:07 exercise.pdf]][[Solutions 7 >>attach:07 exercise solutions.pdf]]
42 [[Exercises 8 >>attach:08 exercise.pdf]][[Solutions 8 >>attach:08 exercise solutions.pdf]]
43 [[Exercises 9 >>attach:09 exercises.pdf]][[Solutions 9 >>attach:09 exercise solutions.pdf]]
44 [[Exercises 10 >>attach:10 exercise.pdf]][[Solutions 10 >>attach:10 exercise solutions.pdf]]
45 [[Exercises 11 >>attach:11 exercise.pdf]][[Solutions 11 >>attach:11 exercise solutions.pdf]]
46 [[Exercises 12 >>attach:12 exercise.pdf]][[Solutions 12>>attach:12 exercise solutions.pdf]]
47
48 === Lectures ===
49
50 Weeks 36-42 and 44-50, Wednesday 10-12 in room B321, Friday 11-13 in room B322. Two hours of exercise classes per week.
51
52 === Exams ===
53
54 Final exam. Also bonus points for the exercises: 25% - 1 point, 40% - 2 points, 50% - 3 points, 60% - 4 points, 75% - 5 points.
55
56 === Bibliography ===
57
58 Allen Hatcher: Algebraic Topology
59
60 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57240||shape="rect"]] ===
61
62 Did you forget to register? [[What to do>>doc:mathstatOpiskelu.Kysymys4]].
63
64 === Exercise groups ===
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66 |=(((
67 Group
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69 Day
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71 Time
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73 Place
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75 Instructor
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78 1.
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80 Tuesday
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82 12-14
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84 C322
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86 Aleksandr Pasharin
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