Nullification Writhe and Chirality of Alternating Links

Abstract

In this paper, we show how to split the writhe of reduced projections of oriented alternating links into two parts, called nullification writhe, or wx, and remaining writhe, or wy, such that the sum of these quantities equals the writhe w, and each quantity remains an invariant of isotopy. The chirality of oriented alternating links can be detected by a non-zero wx or wy, which constitutes an improvement compared to the detection of chirality by a non-zero w. An interesting corollary is that all oriented alternating links with an even number of components are chiral, a result that also follows from properties of the Conway polynomial.