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nlin.SI2024
On Symmetries of Finite Geometries
Oliver Knill
The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The sym…
math.CO2024
Morse and Lusternik-Schnirelmann for graphs
Oliver Knill
Both Morse theory and Lusternik-Schnirelmann theory link algebra, topology and analysis in a geometric setting. The two theories can be formulated in finite geometries like graph t…
math.GT2024
Manifolds from Partitions
Oliver Knill
If f maps a discrete d-manifold G onto a (k+1)-partite complex P then H(G,f,P),the set of simplices x in G such that f(x) contains at least one facet in P defines a (d-k)-manifold.