Fall 2017 MATH 276 001 LEC

Topics in Topology
Schedule: 
SectionDays/TimesLocationInstructorClass
001 LECTuTh 11:00AM - 12:29PMEvans 72Ian Agol45434
UnitsEnrollment Status
4Open
Additional Information: 

Prerequisites: Math 250A, Math 215A. Math 143 and Math 214 will be helpful. 

Description:

Examples of invariants of knots and links. 

Knots and links are closed embedded curves in 3-dimensional Euclidean space.

Knot theory describes the classification of knots and their relations to many

related topics. There are a plethora of invariants of knots in order to distinguish

them up to isotopy (continuous deformation preserving the embedding). The

goal of this topics class will be to investigate some of these invariants, hopefully

finding some connections between different invariants and highlighting some open problems. 

 

We will follow roughly the historical/topical order of introduction of these invariants. Examples

will hopefully include: 

 

  • fundamental group
  • Seifert genus
  • Alexander polynomial 
  • geometric decomposition
  • simplicial volume
  • A-polynomial
  • twisted Alexander polynomials
  • Jones polynomial
  • other quantum polynomials (Kauffman, HOMFLYPT, colored variants)
  • Vassiliev invariants
  • Khovanov homology
  • grid link homology

In order to understand some of these invariants, we will have to develop a bit of 

the theories of representing knots, such as projections and Reidemeister moves,

braids, and grid diagrams.  

Office: 921 Evans Hall

Office Hours: 

Required Text: 

Recommended Reading: 

 

"An Introduction to Knot Theory"
by Raymond Lickorish.

 

Grading: Letter grade.

Homework:

 Students will be required to give a presentation at the end of the semester. 

Course Webpage: