Affiliation:
1. College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China
Abstract
We study satellite operations on Brunnian links. First, we find two special satellite operations, both of which can construct infinitely many distinct Brunnian links from almost every Brunnian link. Second, we give a geometric classification theorem for Brunnian links, characterize the companionship graph defined by Budney in [JSJ-decompositions of knot and link complements in [Formula: see text], Enseign. Math. 3 (2005) 319–359], and develop a canonical geometric decomposition, which is simpler than JSJ-decomposition, for Brunnian links. The building blocks of Brunnian links then turn out to be Hopf [Formula: see text]-links, hyperbolic Brunnian links, and hyperbolic Brunnian links in unlink-complements. Third, we define an operation to reduce a Brunnian link in an unlink-complement into a new Brunnian link in [Formula: see text] and point out some phenomena concerning this operation.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory