Algebraic Topology II - 2018

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Moji Hosseinzadeh, 22.08.2018, 11:00-11:30

Prof. Merry asked be whether I want to write on paper or on the blackboard and for convenience I chose paper. Then i could draw my exam sheet out of his hand and had the following

Proof Question 1

• Show that the tensor product satisfies the UP (lemma 24.4)
• Give the definition of a right-exact additive functor and show that tensoring with A is a right-exact functor (Prop. 24.10)

Proof Question 2

• Definition of a weak fibration
• Prove Serre's theorem (Thm 45.16)

Problem Question

• This was about generalising the degree to manifolds - explicitly showing that a map f from your manifold M to B^n/S^{n-1} which is isomorphic to S^n has degree ±1 and then as a second part show, that one can construct maps of degree k for k in Z by composing it with a map g from S^n to S^n, which has degree k.

In general Prof. Merry and Berit are very kind and help a lot when you get stuck. For the Problem Question hand-wavy arguments were fine.