2010/01/29 by Robert G. Todd, Todd, Robert G.
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1001.5297
openalex publication_date 2010/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The W-polynomial is applied in two ways to questions involving the Kauffman bracket of some families of links. First we find a geometric property of a link diagram, which is less than or equal to the twist number, that bounds the Mahler measure of the Kauffman bracket. Second we find a general form for the Kauffman bracket of a link found by surgering in a single rational tangle along n unlinked components, all in a particular annulus. We then give a condition under which the Mahler measure of the Kauffman bracket of such families diverges. We give examples of the condition in action.