User sara - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T17:09:59Z http://mathoverflow.net/feeds/user/11092 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52365/topological-type-of-smooth-manifolds-with-prescribed-homotopy-type-and-pontryagin topological type of smooth manifolds with prescribed homotopy type and pontryagin class sara 2011-01-18T00:23:44Z 2011-01-18T03:27:18Z <p>Can someone help explain the following result:</p> <p>If the dimension is at least five, there are at most finitely many different smooth manifolds with given homotopy type and Pontryagin classes.</p> <p>Thank you so much!</p> http://mathoverflow.net/questions/47749/good-perspective-in-viewing-manifolds-of-infinite-dimension good perspective in viewing manifolds of infinite dimension sara 2010-11-30T02:54:11Z 2010-11-30T03:52:43Z <p>Borel conjectued aspherical closed manifolds are topologically rigid.(i.e.a homotopy equivalence between two aspherical manifolds is homotopic to a homeomorphism).</p> <p>now,soppuse M is a K(G,1) space, it is well known that if G is a finite group,then M should be of infinite dimension.</p> <p>I am not so comfortable with spaces of infinite dimesion. are there some good (natural) prespective in viewing such spaces.</p> http://mathoverflow.net/questions/47380/fundamental-group-and-complete-invariant-of-irreducible-3-manifolds fundamental group and complete invariant of irreducible 3-manifolds sara 2010-11-25T22:05:15Z 2010-11-26T03:01:39Z <p>I heard that,by Perelman's work,we can get that the fundamental group is a complete invariant of irreducible 3-manifolds (except for lens spaces). can someone help explain this.Thank you!</p>