Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
1. TOPICAL OUTLINE
This course will introduce the techniques and methods of geometric topology. Material will be covered from topics such as the topology of 3-dimensional manifoles, hyperbolic geometry and hyperbolic structures and knot theory. As time allows, topics to be covered could include:
1. Topology of 3-dimensional manifolds. Unique factorization, Heegaard diagrams, Dehn surgery, incompressible surfaces, Haken manifolds.
2. Hyperbolic geometry and hyperbolic structures on surfaces and 3-manifolds
3. Knots and knot invariants. Seifert surfaces. Knot polynomials.
4. Surfaces and their diffeomorphisms. Teichmuller spaces.
John Hempel, 3-Manifolds, Annals of Math. Study 86, Princeton University Press, 2004.
Micheal Kapovich, Hyperbolic Manifolds and Discrete Groups, Birkhauser, Boston MA, 2001.
Dale Rolfsen, Knots and Links, Publish or Perish, 1976.
W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics 43, American Mathematical Society, Providence RI, 1980.
WP Thurston, Three-dimensional geometry and topology, Princeton University Press, Princeton NJ, 1997.