# MA3F2 Knot Theory

**Lecturer:** Daan Krammer

**Term(s):** Term 2

**Status for Mathematics students:** List A

**Commitment:** 30 lectures

**Assessment:** 3 hour exam

**Prerequisites:** MA3F1 Introduction to Topology

**Leads To: **MA408 Algebraic Topology and MA447 Homotopy Theory.

**Content**: A knot is a smooth embedded circle in R^3. After a geometric introduction of knots our approach is rather algebraic, heavily leaning on Reidemeister moves.

**Prerequisites**: Little more than linear algebra plus an ability to visualise objects in 3-dimensions. Some knowledge of groups given by generators and relations, and some basic topology would be helpful.

**Books**:

Listed in order of accessibility:

Colin C Adams, *The Knot Book*, W H Freeman, 1994.

Livingston, Charles. *Knot Theory* Washington, DC: Math. Assoc. Amer., 1993. 240 p.

N.D. Gilbert and T. Porter, *Knots and surfaces*, Oxford, Oxford University Press, 1994.

Peter Cromwell, *Knots and Links*, CUP, 2004.

Louis H. Kauffman, *Knots and physics*, Singapore, Teaneck, N.J., World Scientific, 1991 Series on knots and everything, v.1.

Louis H. Kauffman, *On knots*, Princeton, N.J., Princeton University Press, 1987 Annals of mathematics studies, 115.

Dale Rolfsen, *Knots and links*, Berkeley, CA, Publish or Perish, c1976 Mathematics lecture series, 7.

Gerhard Burde, Heiner Zieschang, *Knots*, Berlin, New York, W. De Gruyter, 1985 De Gruyter studies in mathematics, 5.

Lectures from previous years are available on the web.