My Math Forum A question about topological invariant

 Real Analysis Real Analysis Math Forum

 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 n-dimensional manifold to a n+1-dimensional 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 one-to-one 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.

 Tags invariant, question, topological

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post HubertM Real Analysis 1 January 19th, 2014 02:19 PM golomorf Real Analysis 4 February 1st, 2013 08:24 AM sdj Computer Science 0 October 28th, 2012 10:06 PM mami Linear Algebra 0 April 27th, 2012 03:11 PM tinynerdi Linear Algebra 0 April 11th, 2010 11:48 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top