Agol's proof of the [Virtual Haken conjecture][1] was a wonderful application of the tools developed by Wise and his coauthors in geometric group theory to 3-manifold topology.  The Virtual Haken conjecture, which can be thought of as the topological classification of compact 3-manifolds, is a fundamental result.

Agol's theorem:

> Every cubulable hyperbolic group is virtually special.

also has other dramatic consequences for hyperbolic groups.  It's arguably the most important theorem proved in both algebra *and* topology in the last five years.


  [1]: http://www.math.uiuc.edu/documenta/vol-18/vol-18-eng.html