Chains and Tangles

These two links have homeomorphic exteriors.

chaintangles001 chaintangles002

They’re both strongly invertible. Let’s quotient the first link by its strong inversion to get a tangle. Then we’ll isotop that tangle around and eventually take its double branched cover to get the second.

chaintangles01

chaintangles02-1

chaintangles02

chaintangles03

chaintangles04

chaintangles05

chaintangles06

chaintangles07

chaintanglesA

chaintanglesB

chaintangles08

chaintangles09

chaintangles10

chaintangles11

chaintangles12

chaintangles13

chaintangles14

chaintangles15-1

chaintangles15

chaintangles16

Notice that this homeomorphism swaps the red and blue meridians and longitudes.

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~ by Ken Baker on February 1, 2012.

3 Responses to “Chains and Tangles”

  1. [...] Ken Baker: Chains and Tangles [...]

  2. Wow. I have no idea what you’re trying to do here, but I like it!

  3. you should add a ‘share on fb’ button to your posts.

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