Project Page for Joseph Walsh and Matthew Meola

 

 

Students:                    Joseph Walsh, Rutgers University

Matthew Meola, Rutgers University

 

Email:                         mathgst4@math.rutgers.edu

 

Faculty Advisor:         Dr. Christopher Woodward

 

Project:           A Study of Knot and Tangle Invariants

 

 


Knots and Tangles, Isotopy and Reidemeister

        What is a knot?

        What is a tangle?

        When are two knots equivalent?

        What are the Reidemeister moves?

 

Basic Category Theory and Chain Complexes

        What is a category?

        What is a functor?

        What are a chain complex and a homology group?

 

Knot Invariants: The Jones Polynomial and Khovanov Homologies

        What is a knot invariant and why are they useful?

        What is the Jones polynomial and how is it calculated?

        What is the Khovanov homology and how is it an improvement over the Jones polynomial?