CHIRALITY OF ALTERNATING KNOTS IN S × I.

In this paper, we will explore the properties of knots that lie in a surface cross an interval. We show that any alternating knot nontrivially embedded in S × I is chiral. This demonstrates that knots in S × I behave differently from knots in the three sphere, where alternating knots (like the figure eight) can be amphichiral. We use a generalized Kauffman bracket polynomial, as well as geometric and covering space techniques. [ABSTRACT FROM AUTHOR]