Dehn-Sommerville and Gauss-Bonnet

These are some slides about a new approach to the Dehn-Sommerville relations.
See arxiv.org/abs/...
Some fixes: 1) Blackmountain operated until 1957, not the sixties. 2) On demo example 1, (11,39,56,28).(1,-1,1,-1), the last minus sign was missing. 3) On demo example 3) spoken: Dehn-Sommerville only works for some not all 5-dimensional varieties (it is required that unit spheres have Euler characteristic 2, this is not the case for all varieties). It works for all 5 dimensional manifolds as mentioned there. 4) Max Dehn discovered the relations also in dimension 5. 5) On the slide ``2D: Descartes-Euler" 2*324-3*215=0 (=0 was missing). 6) There is a mix-up with f(x+1/2) and f(x-1/2) at some point. The function f satisfies the Dehn-Sommerville condition if f is symmetric around the point (-1/2,0) like (x+1/2). This means that f(x-1/2) is even or odd or that f(x)=g(x+1/2) with even or odd g. (I myself often worked in the coordinate system where (-1/2,0) is the origin, where the symmetry can be seen better).