most recent 30 from http://mathoverflow.net 2013-05-25T04:58:23Z http://mathoverflow.net/feeds/user/8188 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/34848/are-topological-manifolds-homotopy-equivalent-to-smooth-manifolds Jake 2010-08-07T16:34:42Z 2012-04-02T11:19:18Z

<p>There exist topological manifolds which don't admit a smooth structure in dimensions > 3, but I haven't seen much discussion on homotopy type. It seems much more reasonable that we can find a smooth manifold (of the same dimension) homotopy equivalent to a given topological manifold. Is this true, or is there a counterexample?</p>

http://mathoverflow.net/questions/34658/is-there-a-whitney-embedding-theorem-for-non-smooth-manifolds Jake 2010-08-05T17:20:50Z 2011-08-11T15:31:33Z

<p>For smooth $n$-manifolds, we know that they can always be embedded in $\mathbb R^{2n}$ via a differentiable map. However, is there any corresponding theorem for the topological category? (i.e. Can every topological manifold embed continuously into some $\mathbb R^N$, and do we get the same bound for $N$?)</p>