Final paper

• Your final paper should present, in an expository way, a topic related to but not covered in the course.
• The final paper should be about 10-20 pages.
• Papers typeset in TeX are weclome!
• A short paper showing you have understood a topic thoroughly is the best.
• Try to make your treatment as concrete as possible -- include examples as well as theory. The more focused the better.
• An outline of your final paper, with references, is due on Monday, 24 November.
• The final paper is due on the last day of the course, 15 December.
• You will present your final project to the class during the last 2 meetings of the course, 7 and 15 December.

Some Possible Topics

• The Jordan Curve Theorem and the Schoenflies Theorem
• Immersed loops in the plane (Whitney)
• Embedded / immersed surfaces in space
• Hyperbolic groups (Gromov)
• The boundary of a group
• Unsolvable problems in group theory
• The modular group SL ₂(Z) and the groups SL ₂(Z/n)
• Hyperbolic geometry of surfaces
• Circle bundles over surfaces and the Hopf invariant
• Simple closed curves on surfaces
• The figure eight knot complement
• Fibered knots
• Vasilliev invariants
• Hyperbolic volume as a knot invariant
• Wild knots, Antoines' necklace and the Alexander horned sphere
• Dehn's Lemma and/or the Loop Theorem

Midterm paper

• The midterm paper is a warmup to the final. It should present a concise exposition of a topic that has been discussed or touched on in class.
• The midterm paper should be about 5-10 pages.
• The midterm paper will be due on 3 November 2003.