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December 21st, 2012, 04:38 AM  #1 
Newbie Joined: Dec 2012 Posts: 10 Thanks: 0  A question about topological invariant
Hi, I'm a physicist and have a question. Is it possible to change the dimensionality of a manifold while its topology remains unchanged? If yes, what kind of topological invariant supports such a transformation? Thank you all. 
December 21st, 2012, 07:56 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: A question about topological invariant
What do you mean by "change the dimensionality of a manifold"?

December 21st, 2012, 08:35 AM  #3 
Newbie Joined: Dec 2012 Posts: 10 Thanks: 0  Re: A question about topological invariant
changing number of dimensions of manifold; I search for a topological invariant, if exists, which allows to transform a ndimensional manifold to a n+1dimensional one.

December 21st, 2012, 11:28 AM  #4 
Newbie Joined: Dec 2012 Posts: 10 Thanks: 0  Re: A question about topological invariant
I think that I find the answer. Topological invariants remain unchanged under homeomorphism. however, it is impossible to define a homeomorphism between two manifolds of different dimensions since such a mapping is not onetoone and therefore the mapping is not invertible (while a homeomorphism must be). If this argument is true, it then cannot be defined any topological invariant when the number of dimension of manifold changes.


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invariant, question, topological 
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