Flat plumbing basket and contact structure
Tetsuya Ito, Keiji Tagami
TL;DR
This paper explores the relationship between flat plumbing baskets, a type of Seifert surface, and contact structures supported by open book decompositions, providing bounds and exact numbers for various knots and links.
Contribution
It establishes connections between flat plumbing baskets and contact structures, and computes flat plumbing basket numbers for specific knots and links.
Findings
Lower bounds for flat plumbing basket numbers derived.
Exact flat plumbing basket numbers determined for certain knots and links.
Connections between Seifert surfaces and contact topology clarified.
Abstract
A flat plumbing basket is a Seifert surface consisting of a disk and bands contained in distinct pages of the disk open book decomposition of the 3-sphere. In this paper, we examine close connections between flat plumbing baskets and the contact structure supported by the open book. As an application we give lower bounds for the flat plumbing basket numbers and determine the flat plumbing basket numbers for various knots and links, including the torus links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · semigroups and automata theory