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pro vyhledávání: '"Knill, Oliver"'
Autor:
Knill, Oliver
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 simplices cover $G$. Each of these curvatures can be written as an expect
Externí odkaz:
http://arxiv.org/abs/2409.01425
Autor:
Knill, Oliver
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 symmetry is a subset of the orthogonal group or unitary group and isospec
Externí odkaz:
http://arxiv.org/abs/2408.13973
Autor:
Knill, Oliver
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 that intersect. If K,U is a closed-open pair in G, we prove here a quad
Externí odkaz:
http://arxiv.org/abs/2406.17214
Autor:
Knill, Oliver
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 theory or within finite abstract simplicial complexes. We work here mos
Externí odkaz:
http://arxiv.org/abs/2405.19603
Autor:
Knill, Oliver
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.
Comment: 12 pages, 8 figures, added more code and statistics exa
Comment: 12 pages, 8 figures, added more code and statistics exa
Externí odkaz:
http://arxiv.org/abs/2401.07435
Autor:
Knill, Oliver
A discrete d-manifold is a finite simple graph G=(V,E) where all unit spheres are (d-1)-spheres. A d-sphere is a d-manifold for which one can remove a vertex to make it contractible. A graph is contractible if one can remove a vertex with contractibl
Externí odkaz:
http://arxiv.org/abs/2312.14671
Autor:
Knill, Oliver
A theorem of Hakimi, Mitchem and Schmeichel from 1996 states that the edge arboricity arb(G) of a graph is bounded above by the acyclic chromatic number acy(G). We can improve this HMS inequality by 1, if acy(G) is even. We review also results about
Externí odkaz:
http://arxiv.org/abs/2311.03049
Autor:
Knill, Oliver
The arboricity of a discrete 2-sphere is always 3. The arboricity of any other discrete 2-dimensional surface is always 4. For d-manifolds of dimension larger than 2, the arboricity can be arbitrary large and must be larger than d.
Comment: 12 p
Comment: 12 p
Externí odkaz:
http://arxiv.org/abs/2310.14445
Autor:
Knill, Oliver
We prove that every 2-sphere graph different from a prism can be vertex 4-colored in such a way that all Kempe chains are forests. This implies the following three tree theorem: the arboricity of a discrete 2-sphere is 3. Moreover, the three trees ca
Externí odkaz:
http://arxiv.org/abs/2309.01869
Autor:
Knill, Oliver
If T is an ergodic automorphism of a Lebesgue probability space (X,A,m), the set of coboundries B = db =T(b)+b with symmetric difference + form a subgroup of the set of cocycles A. Using tools from descriptive set theory, Greg Hjorth showed in 1995 t
Externí odkaz:
http://arxiv.org/abs/2307.12476