## MT 832: Combinatorial Methods in Low-Dimensional Topology

### Spring 2019

**Time:** M/W 10:30-11:50

**Location:** Maloney 536

**Professor:** Josh Greene

**Office:** Maloney 527

** Course description: **
To appear.

**Lecture Notes:**

Lecture 1. Introduction to the knot complement problem.

Lecture 2. The Gordon-Luecke framework, part 1.

Lecture 3. The Gordon-Luecke framework, part 2.

Lecture 4. The Gordon-Luecke framework, part 3.

Lecture 5. The Gordon-Luecke framework, part 4, and thin position, part 1.

Lecture 6. Thin position, part 2.

Lecture 7. Thin position, part 3.

Lecture 8 (in preparation). Thin position, part 4.

Lecture 9 (in preparation). Thin position, part 5.

Lecture 10. Combinatorial optimization, part 1.

Lecture 11. Combinatorial optimization, part 2.

Lecture 12. Combinatorial optimization, part 3, and Cerf theory and the curve complex, part 1.

Lecture 13. Cerf theory and the curve complex, part 2, and the Fary-Milnor theorem.

Lecture 14. Graph theory, part 1: review, examples, and the index.

Lecture 15. Graph theory, part 2: index properties.

Lecture 16. Graph theory, part 3: bounding Δ and avoiding the trivial type.

**Problem Sets:**

PS1