Differential Geometry

Math in Moscow, Spring 2013

Slides

• Lecture 1: Smooth manifolds: introduction
• Lecture 2: Sheaves, smooth manifolds and locally finite covers
• Lecture 3: Partition of unity.
• Lecture 4: Hausdorff dimension and Hausdorff measure.
• Lecture 5: Vector fields and derivations.
• Lecture 6: Germs and the sheaf of derivations.
• Lecture 7: Locally free fibrations and categories.
• Lecture 8: Locally free fibrations and vector bundles.
• Lecture 9: Serre-Swan theorem.
• Lecture 10: De Rham algebra.
• Lecture 11: Lie derivative.
• Lecture 12: Poincare lemma.

• Handout 1: smooth manifolds, sheaves, partition of unity (February 4).
• Handout 2: Remedial topology (February 11).
• Handout 3: Hausdorff dimension and measure (February 18).
• Handout 4: Germs, direct limits and soft sheaves. (February 25).
• Handout 5: Vector fields and derivations. (March 4).
• Handout 6: Vector bundles and sheaves. (March 11).
• Handout 7: Fibrations and categories. (April 1).
• Handout 8: Tensor product and dual bundle. (April 8).
• Handout 9: Serre-Swan theorem (April 15).
• Handout 10: de Rham algebra (April 22).
• Handout 11: Lie derivatives and Poincare lemma. (April 29).

• Test assignment #1, 04.02.2013 (results)
• Test assignment #2, 18.03.2013 (midterm). Results.
• Exam problems [ randomizer ]
• Mark sheet for handouts 1 and 2.
• Mark sheet for handouts 3, 4, 5.
• Mark sheet for handouts 6, 7, 8.
• Final results for the course (updated).

You may contact me through verbit[]mccme.ru

Laboratory of Algebraic Geometry and its Applications