Syllabus:  MT 8832  Geometry/Topology IV: Surfaces and branched surfaces in 3-manifolds

Spring 2018

Course Description:
MT8832 is a research-oriented graduate course on Geometry and Topology. Topics for this course vary each year depending on the instructors. Topic this year is 3-manifold topology. I will quickly go cover some basics of 3-manifold topology at the beginning and mostly focus on surfaces, branched surfaces, foliations and laminations in knot exteriors.

Prof. Tao Li;       Office: Maloney 542;   Phone: 617-552-3767;  Email:

Monday 12:00 - 1:45 pm (5-minute break at 12:50), Tuesday 1:00 - 1:50 pm; Maloney Hall 560

Office Hours:

Monday and Tuesday: 9:30 - 11:00 am; Thursday: 3:00 - 4:00 pm
(Other hours available by appointment)
Office: Maloney 542; Phone: 617-552-3767;  Email: taoli


Some references on 3-manifold topology:
Notes on Basic 3-manifold Topology by Allen Hatcher (available at: ).
3-manifold by John Hempel, published by the AMS.
Lectures on Three-manifold Topology by William Jaco, published by the AMS.
Knots and Links by Dale Rolfsen, published by the AMS.

Papers on surfaces, branched surfaces, laminations and foliations:
Incompressible surfaces via branched surfaces. Floyd, W.; Oertel, U. Topology 23 (1984), no. 1, 117–125.
On the boundary curves of incompressible surfaces. Hatcher, A. E. Pacific J. Math. 99 (1982), no. 2, 373–377
Incompressible surfaces in punctured-torus bundles. Floyd, W.; Hatcher, A. Topology Appl. 13 (1982), no. 3, 263–282.
Incompressible surfaces in 2-bridge knot complements. Hatcher, A.; Thurston, W.Invent. Math. 79 (1985), no. 2, 225–246.
Laminar branched surfaces in 3-manifolds. Tao Li, Geometry & Topology, 6 (2002), 153--194.
Essential laminations and Dehn surgery on 2-bridge knots. Delman, Charles, Topology Appl. 63 (1995), no. 3, 201–221.
Alternating knots satisfy Strong Property P. Delman, Charles; Roberts, Rachel, Comment. Math. Helv. 74 (1999), no. 3, 376–397.
Constructing essential laminations and taut foliations which survive all Dehn surgeries, Charles Delman, unpublished