Difference between revisions of "Differential Geometry II - 2018"
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Here, I would explain what the Professor's style of exam is and how I felt during the exam, if I would have been awake. | Here, I would explain what the Professor's style of exam is and how I felt during the exam, if I would have been awake. | ||
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| + | == Sebastian, 13.08.18, 10:30-11:00 == | ||
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| + | * No non vanishing vector field on \(S^2\) (with 2 proofs: Hairy Ball and Euler Characteristic) | ||
| + | * Compute Euler characteristic of \(S^2\) (explicitly with the Vector field from the Problem Sheets) | ||
| + | * Show that every smooth map \(\mathbb{CP}^2 \to \mathbb{CP}^2\) has a fixed point. (Lefschetz Trace formula, using the ring structure of \(\mathbb{CP}^2\)) | ||
| + | * Sketch the proof of Lefschetz Trace Formula (Stated the three main steps orally, that was enough). | ||
| + | * Show that \(H^\star(\mathbb{CP^2}) \cong \mathbb{R}[\omega]/\omega^3\) (the Poincaré dual of \(\mathbb{CP}^1\) is the Euler class of \(H\), and \(\omega^2 \neq 0\) | ||
| + | * State and prove Moser Isotopy (I sketched the proof with some problems using Cartan's Formula). | ||
| + | |||
| + | Salamon is very friendly. Whenever I was unsure of at detail he would ask more specific questions until I was sure. | ||
Revision as of 09:31, 13 August 2018
Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like me kicking you with my fists.
Max Muster, 01.01.1990, 11:30-12:00
Topics:
- Pi is transcendental
- Riemann-Hypothesis
- Example for why P=NP
Here, I would explain what the Professor's style of exam is and how I felt during the exam, if I would have been awake.
Sebastian, 13.08.18, 10:30-11:00
- No non vanishing vector field on \(S^2\) (with 2 proofs: Hairy Ball and Euler Characteristic)
- Compute Euler characteristic of \(S^2\) (explicitly with the Vector field from the Problem Sheets)
- Show that every smooth map \(\mathbb{CP}^2 \to \mathbb{CP}^2\) has a fixed point. (Lefschetz Trace formula, using the ring structure of \(\mathbb{CP}^2\))
- Sketch the proof of Lefschetz Trace Formula (Stated the three main steps orally, that was enough).
- Show that \(H^\star(\mathbb{CP^2}) \cong \mathbb{R}[\omega]/\omega^3\) (the Poincaré dual of \(\mathbb{CP}^1\) is the Euler class of \(H\), and \(\omega^2 \neq 0\)
- State and prove Moser Isotopy (I sketched the proof with some problems using Cartan's Formula).
Salamon is very friendly. Whenever I was unsure of at detail he would ask more specific questions until I was sure.
