The Unapologetic Mathematician

Mathematics for the interested outsider

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.

About these ads

March 5, 2007 - Posted by | Uncategorized

No comments yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 386 other followers

%d bloggers like this: