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University of Connecticut Department of Mathematics UConn Math Club |
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| Take a piece of string, jumble it up, then seal the ends together.
The result is a knot. Notice that you can't untie the knot because you've
permanently sealed the ends together. (If we don't jumble at all, we'll just
end up with a circle, which we call the unknot.) We call two knots
equivalent if you can move one jumbled piece of string to look exactly like
the other without cutting it open.
Knots naturally live in 3-space. We'll discuss a different equivalence relation called concordance involving the fourth dimension. A knot that is concordant to the unknot is called a slice knot. I will discuss some joint work with T. Cochran, S. Harvey, and myself that show that knots in a certain family whose slice status was previously unknown are in fact not slice. |
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UConn Math Club Webpage: http://www.math.uconn.edu/mathclub/