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