Branko's M2 Is Brunnian

Rick Mabry and Laura McCormick, Branko's M2 Is Brunnian, Mathematics Magazine, 93, no. 5 (Dec. 2020), 323–329.

• The article on the publisher's website Taylor & Francis Online
• For access to the full article, send me a request at my university address: Richard [period] [my last name] [squiggly "at" symbol] LSUS [dot] edu [nothing further!].

Below are some supplementary bits and pieces related to the article.

• In the article, we promised "a more leisurely version of our proof without words, revealed as a long sequence of images in which the link 'AltM2-minus-one' in Figure 2 is unraveled step-by-step". Here is such a sequence as a simple slideshow of 34 images. There are some instructions there, but it amounts to just paging through a sequence of images.
  
  The sequence shows how (any) six of the seven components of "AltM2" are actually unlinked, in spite of looking like a mess. This is an important part of the proof that the seven-component link is Brunnian. Use your browser controls to set the size of the display (ctrl +/- works in Chrome, for instance). The images are set to be displayed at full size (800 pixels square), so a bit of adjustment will probably be necessary for getting a nice fit on your screen.
  
  Some frame advances will challenge you just a bit, such as when several strands are tugged on at once. Try using the left/right arrow KEYS to rock back and forth to see what has happened at each step.
  
  
• The "Supplement": The technical details promised in the article are in this PDF. It probably isn't the final version, but it has all of the necessary goods and then some.
  
  Please see Section 6 of the supplement for a discussion of "Marilyn's Cross" (and Marilyn). Click here for two "eye candy" renderings of the figures.
  
  For a not-terrible, but imperfect HTML version of the supplement, try this conversion. I find the font size too small, but ctrl+ fixes that for me. Right-clicking an image and opening it elsewhere gets you the original sizes. (I used htlatex within my MiKTeX system, after looking at loads of online help.)
  
  
• We made the cover Taylor & Francis Online!
  
  
• Click for the image of "AltM2" — the Proof Without Words. That's deliberately snarky. But the article itself began that way. The image really is the proof of the existence of Brunnian link whose projection is a symmetric 7-Venn diagram. But seeing that requires a bit of work (and perhaps a few words). We originally submitted that image and this Hint Without Words (along with just a few words) as a one-page note. The editors and referees liked it but thought more actual words would be better and we were invited to "flesh it out" a bit more. Wow, do NOT give wordy people such liberties. Things got out of hand and the article is the result. Many thanks to editors Mike Jones and Jason Rosenhouse and an anonymous referee at Mathematics Magazine for their indulgence.
  
  
• Professor S. Louise Gould at Central Connecticut State University has used the figures in the article as the basis for an artwork. It was presented at the 2021 Bridges Conference. You can see it in the online gallery Bridges.