36 citations · 145 across the 24 of their papers we have counts for
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Characteristic Topological Invariants
Oliver Knill
The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms…
The Sphere Formula
Oliver Knill
The sphere formula states that in an arbitrary finite abstract simplicial complex, the sum of the Euler characteristic of unit spheres centered at even-dimensional simplices is equ…
Finite topologies for finite geometries
Oliver Knill
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Beside…
On Primes, Graphs and Cohomology
Oliver Knill
The counting function on the natural numbers defines a discrete Morse-Smale complex with a cohomology for which topological quantities like Morse indices, Betti numbers or counting…
Graphs with Eulerian unit spheres
Oliver Knill
d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eul…
Coloring graphs using topology
Oliver Knill
Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it…