[Discussion] [VERY Off-Topic!: Ehresmann Connections]

[Thomas Clayton]

Dear Prof. Parker:

I made the mistake of looking at WHAT the PAI ref. was to.

Its first reference, in turn, mentioned "Ehresmann Connections". I was crazy enough to download it and read - well, try to read - (some of) it.

For me, who just had gotten a 'finger hold' (mountain climbing metaphor) on _tangent bundles_ the last time I seriously looked at Math. (three years ago), it looks as if there are ?Tangent Tangent Bundles? (TTM) somehow related to second derivatives - because you mention SODEs. 

Now I - or rather, then I'd - thought I was getting pretty close to the finale (summit) of all this abstraction with this thought: Tangents get you the first D1,C1 level and connections seemed to be the D2,C2 (and higher D3,C3 etc) levels. [i.e. First derivative, second derivative, etc.]. (Riemann, and such, are abstracted to connections, I thought.)

NOW you've got me scratching my head - and wondering (from my cravas(?) perch) just WHERE this climb goes to!

The K. Freeman ~History of Connections~ (ref. 24) looks like an interesting read to me, BTW.


Lastly, and NOT related to your (joint) paper, 
When I was last looking at Math, I had gone to see a paper by Newns and Walker about the requirement relaxation of C'lazy eight' to C1 for 'tangent' spaces. (I can, AND will, get you the exact (London J. Math circa 1955) ref. tomorrow.) This sits on the border between Analysis and Dif'l. Geo./Top.
Do YOU know of any related subject papers?

Sincerely,

Thomas Clayton

BTW, I don't know whether you'll see it (our POSSI list-server may strip it) but I CC:ed my cousin Dave, a retired MN Math Prof. who often is in FL these days. Hence, Dave MN FL.

--- On Tue, 3/2/10, Phil Parker <phil at math.wichita.edu> wrote:

> From: Phil Parker <phil at math.wichita.edu>
> Subject: Re: [Discussion] Hard Drive Partition Sizes
> To: "POSSI Discussion List" <discussion at lists.possi.org>
> Date: Tuesday, March 2, 2010, 1:21 AM

... <snip> ...  <---- BTW, I got this idea from our own, James Cannon!

> 
> -- 
>    Best wishes,
>     Phil Parker
> -----------------------------------------------------------------------------
> URL http://www.math.wichita.edu/~pparker/  
> PAI http://arxiv.org/a/parker_p_1
> Random quote:
>   F u cn rd ths u cnt spl wrth a dm!