22 Nov
2006
22 Nov
'06
7:10 p.m.
On Thursday 23 November 2006 01:48, Fred lunnon wrote:
QUESTION 2: Can every simplicial complex K of dimension n be *affinely* embedded in some Euclidean space? ...
I'm taking "affinely" to mean isometrically, rather than projectively. [I've never managed to work out what people mean by this word --- I gather it might have something to do with having one foot nailed to the origin ...]
"Affine" just means "linear plus constant", or "f(au+bv) = a.f(u)+b.f(v) when a+b=1". It doesn't imply isometric. This is sufficiently well known that I suspect I'm missing some subtlety; is there, for instance, some reason why Dan's question becomes trivial or stupid if "affine" is given its usual meaning? -- g