Thursday May 30 I have to go away, so today (Tuesday) was the last regular lecture this term. The exact syllabus is defined as the material I have been able to cover, and this is listed under "Syllabus, achievement requirements".
We agreed to meet next Thursday, June 6 at the regular time, and I will be available for questions, maybe some recapitulation and problem solving. Hatcher's book has lots of good exercises, ranging from easy to challenging, and I urge you to use them to check that you understand the theory. In addition to the lists of recommended exercises I have given earlier, here are some more:
Ch. 2.2, p.155: 1 - 14
Ch. 2B, p.176: 3, 11
Ch. 3.1, p. 205: 5, 7, 8, 9, 11
Ch. 3.2, p. 229: 1, 3, 4, 6, 11
The exam in MAT4530 will be on Monday June 10, and the last lecture will be Thursday May 30.
I have now started Chepter 3 - Cohomology - and today I finished section 3.1, containing the basic definitions and the part of the theory that is analogous to homology. The main new structure in cohomology is the cup product (section 3.2), and I will start discussing that on Thursday May 16.
The problem set for the mandatory assignment has now been posted, and you find it here. You have two weeks, but it is a good idea to start already now. Please do not hesitate to ask if there is something you don't understand in the text.
For more information on mandatory assignments, see the institute's web pages.
I ended the last lecture before the Easter vacation by formulating Prposition 2.30, but without proof. This section (on degrees of selfmaps of spheres) is fundamental for the definition of Cellular Homology and later applications. The next lecture will be Tuesday, April 2.
Here are some good and instructive exercises from the material we have just covered:
Page 132-33: 17, 26, 27, 28, 29
The compulsory assignment will be posted Thursday April 4. Solutions must then be handed in by Thursday April 18.
Exercises for Tuesday March 5:
- Page 131: 1, 2, 8, 9, 14
We have now finished Chapter 1, where we have covered all the theory before page 77. Tuesday Feb. 19 we start on Chapter 2,
Exercises for Thursday Feb. 14:
- Ch 1.3: 9, 12, 14, 15, 29
Exercises for Tuesday Jan.29:
- Ch 0: 20, 21, 23
- Ch 1.2: 3, 4, 9, 10
The first time-table change was not good for everybody, so we now move the Tuesday lecture to 0815-1000 in room B70. (The good thing is that now all classes are in the same room!)
Starting next week (week 4) the Monday lectures will be moved to Tuesdays 1215-1400 in Room B63. The Thursday lectures are unchanged.