27.11 The exam dates are fixed. Three students will have the exam on Monday 9 Dec.,and the other ones on Tuesday or Wednesday 17-18 Dec. Letters of information will be sent to the students, telling you where to meet and when.
14.11 The two last lectures will be next week, 19 and 21 November (as before).Then we shall finish the covering space theory, and also discuss a little two other famous results at the end of chapter 4, namely the Hurewicz homomorphism, and Van Kampens theorem about the fundamental group, which is an analogue of Mayer-Vietoris in homology.
13.11 The exam dates will be Tuesday and Wednesday, 17-18 December. More later.
5.11 Please fill out the following form for when you can or cannot attend the exam. Deadline for response: 11.11
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22.10 We have now gone through Chapter 3 as much as planned. On Thursday 24 Oct. we start with Chapter 4, on the theory of covering spaces. We will do various things differently, in particular, we shall focus more on group theory and how the covevering space theory can be nicely expressed in terms of the concept of transformation groups.
16.10 Tomorrow Thursday 17 Oct. we start with Chapter 3, called the Eilenberg-Steenrod Axioms. You will see why! But we shall not go into details with the constructions of the tensor product, the functor Hom, and the derived functors Tor and Ext. We shall assume a little familiarity with this and only discuss the basic or general constructions. Much of the material belongs to "homological algebra"
10.10 Tomorrow we start from page 48 (Vick's book), with Prop. 2.12, and will try to go through several propositions and theorems, without detailed proofs. Then we shall try to finish Chapter 2 next week. After that we shall spend a week or so on some of the basic things in Chapter3, before we shall spend the rest of the time we have on Chapter 4 (covering spaces).
1.10 We are in Chap.2, about how to build spaces using attaching maps, about CW-complexes (a special type of spaces built up by attaching cells),and also the construction of the long exact homology sequence for a pair (X,A) of spaces, where A is a subspace of X.
16.9 In the text book we are now on page 24, and will soon finish with chapter 1.Here is an exercise: Use the Mayer -Vietoris sequence to calculate the homology of the Klein bottle. Regard the space as the union of two Moebius bands glued together by a homeomorphism between their boundary circles.(First of all, what would be the spaces U,V and their intersection, when the union of the open sets U and V is the Klein bottle? Consider their homotopy type to determine what are their homology groups)