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Topic: gravity and topology
Replies: 18   Last Post: Jun 30, 2012 11:21 PM

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Posts: 567
Registered: 7/6/11
Re: gravity and topology
Posted: Jun 30, 2012 11:21 PM
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On Jun 30, 8:08 pm, Shmuel (Seymour J.) Metz
<spamt...@library.lspace.org.invalid> wrote:
> In <l-Sdnb2CT9QyznrS4p2d...@giganews.com>, on 06/24/2012
>    at 12:51 PM, Tom Roberts <tjroberts...@sbcglobal.net> said:

> >I forgot to point out that for a manifold with metric (i.e. with
> >geometry), the  topology must be consistent with the curvature of
> >the metric. For instance, the  plane R^2 admits a flat metric
> >(Euclidean geometry), or a metric with negative  curvature
> >(hyperbolic or Lobachevsky geometry), but does not admit a metric
> >with positive curvature (which inherently requires periodicity).

> False. R^2 is diffeomorphic to a patch on a sphere. That
> diffeomorphism gives you a metric on R^2 with positive curvature.
> --
> Shmuel (Seymour J.) Metz, SysProg and JOAT  <http://patriot.net/~shmuel>
> Unsolicited bulk E-mail subject to legal action.  I reserve the
> right to publicly post or ridicule any abusive E-mail.  Reply to
> domain Patriot dot net user shmuel+news to contact me.  Do not
> reply to spamt...@library.lspace.org

Dimension is spherical for gravity and higher for the round 4th

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