# 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,

**Units/Lecture:**

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Prerequisites:**

**Course Description:**

**Suggested Schedule:**

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.

2. READING

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:**

**Assessment:**