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Topic: How do we Evaluate This Form on S^1?
Replies: 11   Last Post: Jan 22, 2013 4:17 PM

 Messages: [ Previous | Next ]
 Bacle H Posts: 283 Registered: 4/8/12
Re: How do we Evaluate This Form on S^1?
Posted: Jan 22, 2013 9:51 AM

On Tuesday, January 22, 2013 6:07:41 AM UTC-8, Seymour J. Shmuel Metz wrote:
> In <lbGdnZWOCuemA2DNnZ2dnUVZ5rmdnZ2d@giganews.com>, on 01/21/2013
>
> at 11:59 AM, "W. Dale Hall" <wdhall@alum.mit.edu> said:
>
>
>

> >Which statement is the "in fact, false" non-sequitur?
>
>
>
> "tangent vectors to different points on S^1 aren't quite identifiable
>
> with one another"
>
>
>

> >I maintain that my first statement is perfectly correct.
>
>
>
> You can maintain it all you want, but it remains false.
>
>
>

> >Otherwise, why would one ever worry about the whole machinery of vector bundles?
>
>
>
> Because in the general case you're not dealing with a flat affine
>
> connection.
>
>
>

> >A beginner needs to learn that the tangent bundle is something
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> >other than a vector space;
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>
>
> For which purpose S^2 is mopre suitable than S^1.
>
>
>

> >I suspect that the OP knows little to nothing about parallel transport.
>
>
>
> It might have been useful to mention it, stressing that what is true
>
> of S^1 is not true in general, even for S^2.
>
>
>

> >Again, I regard it as a pedagogical error to use machinery without
>
>
>
>
> I regard it as a pedagogical error to oversimplify.

Well, you seem to be criticizing a lot but you're not offering anything better;
you're not being very constructive/helpful yourself.
>
>
>
> --
>
> 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 spamtrap@library.lspace.org

Date Subject Author
1/20/13 gk@gmail.com
1/20/13 W. Dale Hall
1/21/13 Shmuel (Seymour J.) Metz
1/21/13 W. Dale Hall
1/21/13 Bacle H
1/21/13 Bacle H
1/22/13 gk@gmail.com
1/22/13 achille
1/22/13 Shmuel (Seymour J.) Metz
1/22/13 Bacle H
1/22/13 Bacle H
1/22/13 gk@gmail.com