Low Dimensional Topology

December 6, 2007

Undergrad research problems?

Filed under: Uncategorized — Jesse Johnson @ 3:08 pm

Now that this blog is starting to get some traffic, I thought I’d take advantage of the comments box by asking if anyone had thoughts on open problems in low dimensional topology that would be suitable for undergrads, in particular something that might work for a summer REU. There seems to have been at least one successful undergraduate project on intrinsically knotted/linked graphs and I saw a presentation by Denise Halverson at last year’s Spring Topology and Dynamics conference about an undergrad. project to find the smallest connected set containing a given collection of points in different geometric surfaces. I’m trying to put together an undergraduate project for this summer having to do with normal loops in triangulated surfaces. (This seems like an approachable problem for someone with minimal background and it might yield some useful ideas for thinking about normal and almost normal surfaces.) Any thoughts on how to find a good undergraduate research project, or what areas of low dimensional topology might have good problems?

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