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
Approved: 2010-05-28,


Offered Winter alternate years; 4 units; 1st LEC 3.0 hrs/wk; 2nd PRB 1.0 hrs/wk

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
See below.


Course 215A

Course Description:

Topology of two- and three-dimensional manifolds. Surfaces and their diffeomorphisms. Dehn twists. Heegaard surfaces. Theroy of 3-dimensional manifolds. Knots and knot theory. Hyperbolic manifolds and geometric structures

Suggested Schedule:


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.

Additional Notes:

216 May be repeated one time for credit.


Student workload is 3 hours of lecture and 9 hours of outside preparation for a total of 12 hours per week.