## More on Analytic Torsion

We report on some progress on analytic torsion A(G) for graphs. A(G) is a positive rational number attached to a network. We can compute it for contractible graphs or spheres.

We report on some progress on analytic torsion A(G) for graphs. A(G) is a positive rational number attached to a network. We can compute it for contractible graphs or spheres.

A major open problem in Riemannian geometry is the classification of even dimensional positive curvature manifolds with symmetry. There is a reduction theory which produces a periodic system of elements. This picture has affinity with gauge bosons in physics.

The Hopf conjectures were first formulated by Hopf in print in 1931. The sign conjecture claims that positive curvature compact Riemannian 2d-manifolds have positive Euler characteristic and that negative curvature compact Riemannian 2d-manifolds have Euler characteristic with sign (-1)d . The product conjecture claims there is no positive curvature metric …