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.
MAT 216: Geometric Topology
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.