The Poincaré Homology Sphere, and Thinking What I’ll Do Next


Yenergy was good enough to write a comment about this, but people might have missed it. “Dodecahedral construction of the Poincaré homology sphere, part II” is up. The post is an illustration trying to describe several pages of the 1979 paper Eight Faces Of The Poincaré Homology 3-Sphere by R C Kirby and M G Sharlemann.

I admit I have to read it almost the same way a non-mathematician would. My education never took me into topology deep enough to be fluent in the notation or the working assumptions behind the paper. I may work my way farther than a non-mathematician, since I’ve been exposed to some of the symbols. The grammar of the argument is familiar. And many points of it are common to fields I did study. Nevertheless, even if you just skim the text, skipping over anything that seems too hard to follow, and look at the illustrations you’ll get something from it.

Past that, I wanted to thank everyone for seeing me into the start of May. I am figuring to give up the post-a-day schedule. It’s exciting to have three thousand-word and four posts of more variable lengths each week, but I need to relax that schedule some. I am considering, based on the conversation I got into with Elke Stangl about the Yukawa Potential, whether to do a string of essays about closed orbits. That would almost surely involve many more equations than is normal around here. But it could make for a nice change of pace.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

2 thoughts on “The Poincaré Homology Sphere, and Thinking What I’ll Do Next”

  1. The more years spent studying maths the happier one becomes as one realises that on at least the first reading one can skip ALL the “math” and jst read the text. If that doesn’t make any sense the symbols will only make things worse!

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    1. That is the piece that took me longest to learn, really. I think the bad habit comes from textbooks where, so often, the real work is done in a string of equations and the text surrounding it is meaningless or at least uninsightful. (“Now we move x to the left side” … thanks, saw that, but why ‘x’ and why the left side?)

      Reading the text, at least when it explains what the thinking is, gets the lay of the land. Then the details have something to cling to.

      Liked by 1 person

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