Cube Complexes, 3-manifolds, and the Virtual Haken Theorem

Start: 04/29/2014 - 4:15pm
End  : 04/29/2014 - 4:15pm


Timothy Hsu (San Jose State University)


The Virtual Haken Conjecture was, until recently, probably the biggest open problem in $ 3 $--manifolds
($ 3 $-dimensional geometry).  Then in March 2012, Ian Agol proved the conjecture by completing a key part of Dani Wise's program of studying nonpositively curved cube complexes.  So how did questions in $ 3 $-dimensional geometry end up being resolved using spaces made from (very high--dimensional) cubes?  We'll give an overview explaining the connection and describe the speaker's joint work with Wise that is part of the emerging and rapidly growing subject of cube complexes.

Background: This talk is meant to be accessible to students who have had one semester of abstract algebra.  No background in topology is required, and we will give at least cartoon definitions of the relevant technical terms (e.g., $ 3 $-manifold).

Shanahan 3460 (the SkyCube), Harvey Mudd College

Misc. Information

Refreshments at 3:45 p.m. 3rd Floor North Patio of Shanahan & wine and cheese after the talk on the 3rd Floor North Patio of Shanahan

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