45 citations · 674 across the 102 of their papers we have counts for
8 papers · 1 filter
The Three Tree Theorem
Oliver Knill
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: th…
On the cohomology of measurable sets
Oliver Knill
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.…
Weierstrass elliptic functions for the pendulum
Oliver Knill
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendul…
Cohomology of open sets
Oliver Knill
If G is a finite abstract simplicial complex and K is a subcomplex of G and U=G-K is the open complement of K in G, the Betti vectors of K and U and G satisfy the inequality b(G) l…
Spectral monotonicity of the Hodge Laplacian
Oliver Knill
If K,G are finite abstract simplicial complexes and K is a subcomplex of G then the eigenvalues of the Hodge Laplacian of K are smaller or equal than the eigenvalues of the Hodge L…
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…