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: firstname.lastname@example.org
Monday 12:00 - 1:45 pm (5-minute break at 12:50), Tuesday 1:00 - 1:50 pm; Maloney Hall 560
Monday and Tuesday: 9:30 - 11:00 am; Thursday: 3:00 - 4:00
Some references on 3-manifold topology:
Notes on Basic 3-manifold Topology by Allen Hatcher (available at: http://www.math.cornell.edu/~hatcher/3M/3Mdownloads.html ).
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
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Constructing essential laminations and taut foliations which survive all Dehn surgeries, Charles Delman, unpublished