18.904 Written report component

The written report is an introduction to writing and research in mathematics. It should be a pedagogical introduction to a topic which interests you in algebraic topology and which is accessible from the topics covered in the seminar. The document must be approximately 10 pages long and it must be produced with the standard mathematics typsetting software, LaTeX. Here is a template (PDF) I prepared for the report, which you may or may not want to use.

Deadline for choosing topic (email or tell me in person): March 8.

Deadline for first draft (submit by email, including .tex and .PDF file): April 13.

I will make corrections/comments. Deadline for final draft, incorporating corrections/comments (submit by email, include .tex and .PDF file): Monday, April 30.

Suggestions for topics:

Feel free to discuss with me any ideas or interests you may have. You might also take a look at the following lists of ideas: from Mark Behrens and Olga Plamenevskaya (Warning: These are pages from previous years, dates and deadlines do not apply) I'll also update this page to add some more ideas:

• Topological groups: what happens when you combine the idea of a group and a topological space?
• Fiber bundles: these important structures look locally like a product of two spaces but may possess a different global structure (for example, the Möbius band is a nontrivial fiber bundle which looks locally like a product of intervals).
• The De Rham complex: A fundamental link between algebraic topology and differential geometry.
• Cech/Sheaf cohomology: A convenient conceptual and calculational tool for computing cohomology.
• Complex line bundles on 2-dimensional surfaces. How to classify them and give interesting examples.
• Morse theory: determine important topological properties of a manifold by studying the critical points of a real-valued function on it.
• Orbifolds and groupoids; the fundamental groupoid.