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July 27, 2016

Topological Crystals (Part 2)

Posted by John Baez

k4_crystal

We’re building crystals, like diamonds, purely from topology. Last time I said how: you take a graph XX and embed its maximal abelian cover into the vector space H 1(X,ℝ)H_1(X,\mathbb{R}).

Now let me back up and say a bit more about the maximal abelian cover. It’s not nearly as famous as the universal cover, but it’s very nice.

Continue reading “Topological Crystals (Part 2)” …
Posted at 10:30 AM UTC | Permalink | Followups (6)

July 23, 2016

Topological Crystals (Part 1)

Posted by John Baez

k4_crystal

Over on Azimuth I posted an article about crystals:

In the comments on that post, a bunch of us worked on some puzzles connected to ‘topological crystallography’—a subject that blends graph theory, topology and mathematical crystallography. You can learn more about that subject here:

I got so interested that I wrote this paper about it, with massive help from Greg Egan:

I’ll explain the basic ideas in a series of posts here.

Continue reading “Topological Crystals (Part 1)” …
Posted at 8:18 AM UTC | Permalink | Followups (10)