45 citations · 674 across the 102 of their papers we have counts for
8 papers · 1 filter
Complexes, Graphs, Homotopy, Products and Shannon Capacity
Oliver Knill
A finite abstract simplicial complex G defines the Barycentric refinement graph phi(G) = (G,{ (a,b), a subset b or b subset a }) and the connection graph psi(G) = (G,{ (a,b), a int…
Green functions of Energized complexes
Oliver Knill
If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the…
Division algebra valued energized simplicial complexes
Oliver Knill
We look at connection Laplacians L,g defined by a field h:G to K, where G is a finite set of sets and K is a normed division ring which does not need to be commutative, nor associa…
Positive curvature and bosons
Oliver Knill
Positive curvature and bosons Compact positive curvature Riemannian manifolds M with symmetry group G allow Conner-Kobayashi reductions M to N, where N is the fixed point set of th…
On a theorem of Grove and Searle
Oliver Knill
A theorem of Grove and Searle directly establishes that positive curvature 2d manifolds M with effective circular symmetry group of dimension 8 or less have positive Euler characte…
A Dehn type quantity for Riemannian manifolds
Oliver Knill
We look at the functional Y(M) = int_M K(x) dV(x) for compact Riemannian 2d-manifolds M, where K(x) = (2d)! (d!)^-1 (4pi)^-d int_T prod_k=1^d K_t_2k,t_2k+1(x) dt involves products…