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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
<> wrote:
> In <>, on 06/24/2012
>    at 12:51 PM, Tom Roberts <> 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  <>
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> reply to

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

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