Presentation Title

Khovanov homology and wrap-arounds: looking for patterns

Advisor Information

Robert Todd

Location

Dr. C.C. and Mabel L. Criss Library

Presentation Type

Poster

Start Date

6-3-2015 2:00 PM

End Date

6-3-2015 3:30 PM

Abstract

Knot theory is the study of knots similar to those we encounter in everyday life. Two primary questions in knot theory are when can two knots be considered equivalent and how do we tell if they are. Mathematicians have invented many tools, called knot invariants, to answer these questions. A knot invariant is a property of a given knot that does not change when you manipulate the knot without cutting the strands. Examples of knot invariants are the crossing number, the Alexander polynomial, and the Khovanov homology. In this project, we study the Khovanov homology of a family of knots and propose a general form of the Poincare polynomial.

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COinS
 
Mar 6th, 2:00 PM Mar 6th, 3:30 PM

Khovanov homology and wrap-arounds: looking for patterns

Dr. C.C. and Mabel L. Criss Library

Knot theory is the study of knots similar to those we encounter in everyday life. Two primary questions in knot theory are when can two knots be considered equivalent and how do we tell if they are. Mathematicians have invented many tools, called knot invariants, to answer these questions. A knot invariant is a property of a given knot that does not change when you manipulate the knot without cutting the strands. Examples of knot invariants are the crossing number, the Alexander polynomial, and the Khovanov homology. In this project, we study the Khovanov homology of a family of knots and propose a general form of the Poincare polynomial.