Algebraic Topology II - 2019
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Joel, 26.08.2019 9:30-10:00
1. Define Cohomology with compact supports.
2. Calculate \( H_c^*(\mathbb{R}^n;G) \).
3. Does a map \(f:X \rightarrow Y\) induce a map \(f^* : H_c^*(Y;G) \rightarrow H_c^*(Y;G)\) ?
4. Do homotopic spaces have the same cohomologies with cpt support?
5. Is the cup product well defined on cohomology with cpt support?
6. State the Poincaré duality theorem for (not neccesarrily cpt) manifolds.
7. Show that \(H_c^i(X \times \mathbb{R};G) = H_c^{i-1}(X;G) \).
