**Project Page for Joseph Walsh and Matthew Meola**

**Students: **Joseph
Walsh,

Matthew Meola,

**Email: **mathgst7@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?