Originally posted by marcus
Stuff about Synge's theorem is available by google on web.

is it? i got nothing by google, except for some course syllabi. wholly uninformative.
i also didn t see it anywhere in my geometry book, neither do Carmo, nor Petersen.
i would be interested to know what it is too, if anyone knows.
as far as Mike2 s description goes, it sounds a lot like the Gaussbonnet theorem, which i know quite well. it states that the integral of the Gaussian curvature over a hyperspace gives you the euler character of the manifold, which is essentially the genus.