Jon Perry writes: << ... if we consider n-manifolds as spaces constructed from n-1-manifolds, then the n-manifold is formed by a continous expansion of varying n-1-mainfolds. ...
There are any number of things that this could mean. Could you spell out what you mean by each of these two clauses? Thanks, Dan
Take an n-manifold, as topologists like to consider surfaces rather than content, this space may be viewed as a varying n-1-m over the n-th dimension. The topological nature of the n-1-m's determines the nature of the n-manifold. Taken over ALL possible basis, the Poincare conjecture is reduced to a simple class clause, which given Smales and others results, reduces the problem to a finite cluase, hence the PC is true. LOL. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com]On Behalf Of asimovd@aol.com Sent: 10 October 2003 00:28 To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Rational Group Jon Perry writes: << ... if we consider n-manifolds as spaces constructed from n-1-manifolds, then the n-manifold is formed by a continous expansion of varying n-1-mainfolds. ...
There are any number of things that this could mean. Could you spell out what you mean by each of these two clauses? Thanks, Dan
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Jon Perry