## November 13, 2006

### Quantization and Cohomology (Week 5)

#### Posted by John Baez

Still catching up… here are the notes for the Halloween class on Quantization and Cohomology:

• Week 5 (Oct. 31) - The canonical 1-form $\alpha$ on $T^* X$. Symplectic structures. Why a symplectic structure should be a nondegenerate 2-form (so we get time evolution from a Hamiltonian) and closed (so time evolution preserves this 2-form). The action expressed in terms of the canonical 1-form.
• Homework: show that if $\alpha$ is the canonical 1-form on the cotangent bundle of a manifold, then $\omega = -d\alpha$ is a nondegenerate 2-form.
Last week’s notes are here; next week’s notes are here. Posted at November 13, 2006 7:48 AM UTC

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