What is the biggest unsolved problem in topology

1. Feb 22, 2008

kurt.physics

What is the biggest unsolved problem in topology

Last edited by a moderator: Mar 8, 2013
2. Feb 23, 2008

CRGreathouse

The Poincaré conjecture for differentiable 4-manifolds? (As opposed to the Poincaré conjecture for 3-manifolds, which Perelman solved.)

3. Feb 23, 2008

kurt.physics

Could you explain the Poincaré for 4-manifolds? Is it harder to prove than 3-manifolds?

4. Feb 23, 2008

mathwonk

wasnt that proved by freedman in around 1980?

5. Feb 24, 2008

CRGreathouse

Friedman showed it for topological 4-manifolds in 1982, but the case of differentiable 4-manifolds is still open as far as I know.

And I really don't know much about topology, I was just throwing out an answer.