We will discuss the problem of recognizing topological manifolds among topological spaces, beginning with classical results, such as Bing’s sphere characterization theorem:
“If a compact, connected, locally connected metric space X is separated by every simple closed curve but by no pair of points, then X is homeomorphic to $S^2$.”
and proceeding to generalizations and open problems. Highlights include the Andrews-Curtis paper on N-space modulo an arc, Edwards-Canon's proof of the double suspension theorem, the Edwards-Quinn characterization of topological manifolds in dimensions at least 5, and current work on understanding counterexamples to Canons conjecture.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5019