4 papers · 1 filter
Remarks about Connection and Dirac matrices
Oliver Knill
The connection Laplacian L and the Dirac matrix D are both n x n matrices defined from a given finite simplicial complex G with n sets. In both cases, there is interlacing of the e…
Geodesics for Discrete manifolds
Oliver Knill
The geodesic flow on a finite discrete q-manifold with or without boundary is defined as as a permutation of its ordered q-simplices. This allows to define geodesic sheets and a no…
Gauss-Bonnet for Form Curvatures
Oliver Knill
We look at curvatures that are supported on k-dimensional parts of a simplicial complex G. These curvature all satisfy the Gauss-Bonnet theorem, provided that the k-dimensional sim…
Fusion inequality for quadratic cohomology
Oliver Knill
Classical simplicial cohomology on a simplicial complex G deals with functions on simplices x in G. Quadratic cohomology deals with functions on pairs of simplices (x,y) in G x G t…