New Turaev Paper

Turaev has just posted a new paper on the arXiv. The abstract says he introduces a sort of cobordism relation for knots in thickened surfaces.

The “thickened surfaces” bit means that instead of putting them into space we put them into some (possibly complicated) surface that’s just thick enough for the strands to get past each other without touching. Imagine wrapping a string around a donut. Not only can the string tangle up with itself, but it also can circle the donut in many different ways. If the donut weren’t there, lots of these donut-knots would be the same, but since we can’t pull the string through the donut they aren’t the same in this setup.

The word “cobordism” is harder to explain. When I get to more about knots in general I’ll eventually get to it. Still, it’s worth a look if you know some topology or you just want to see what a knot theory paper looks like. Turaev is a really big name, and I’m looking forward to a chance to sit down and work through this latest offering.

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