Flat plumbing basket, self-linking number and Thurston-Bennequin number
Abstract
A flat plumbing basket is a surface consisting a disk and finitely many bands which are contained in distinct pages of the trivial open book decomposition of S3. In this paper, we construct a Legendrian link from a flat plumbing basket, and we describe a relation among the self-linking number, the Thurston-Bennequin number and the flat plumbing basket number of the link. As a corollary, we determine the flat plumbing basket numbers of torus links.
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