1. Background & Purposes

Laying the foundation for the study of knots and 3-manifolds, and introducing new knowledge on current research on these areas.

2. Outline & Descriptions

Introduction to knot theory:

(1)  Fundamentals of knots and links

(2)  Seifert surfaces and Alexander polynomial

(3)  Jones polynomial

(4)  Dehn surgery

Introduction to 3-manifolds:

(1)  Dehn’s lemma and loop theorem, sphere theorem, and their applications

(2)  Heegaard splittings and connected sum decomposition

(3)  Seifert fibered manifold

3. Grading

Class attendance

4. Prerequisites

Topology and algebraic topology including some knowledge of homology, homotopy and presentation of group.

5. Registration

https://forms.gle/Z7YjZrzk62kN9Vgg6

6. Course Video

https://www.youtube.com/playlist?list=PLQZfZKhc0kiDgNnwBlFhvsYZT_-qtXYS5