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Hopf plumbing, arborescent Seifert surfaces, baskets, espaliers, and homogeneous braids by Rudolph, Lee is a scholarly article available to read on EtoBox.

What is Hopf plumbing, arborescent Seifert surfaces, baskets, espaliers, and homogeneous braids about?

Four constructions of Seifert surfaces - Hopf plumbing, arborescent plumbing, basketry, and T-bandword handle decomposition - are described, and some interrelationships found, e.g.: arborescent Seifert surfaces are baskets; Hopf-plumbed baskets are precisely homogeneous T-bandword surfaces. A Seifert surface is Hopf-plumbed if it is a 2-disk D or if it can be constructed by plumbing a positive or negative Hopf annulus A(O,-1) or A(O,1) to a Hopf-plumbed surface along a proper arc. A Seifert surface is a basket if it is D or it can be constructed by plumbing an n-twisted unknotted annulus A(O,n) to a basket along a proper arc in D. A Seifert surface is arborescent if it is D, or it is A(O,n), or it can be constructed by plumbing A(O,n) to an arborescent Seifert surface along a transverse arc of an annulus plumband. Every arborescent Seifert surface is a basket. A tree T embedded in the complex plane C determines a set of generators for a braid group. An espalier is a tree in the closed lower halfplane with vertices on the real line R. If T is an espalier then words b in the T-generators correspond nicely to T-bandword surfaces S(b). (For example, if I is an espalier with an edge fro

Author

Rudolph, Lee

Published

1998

Language

EN