45 citations · 674 across the 102 of their papers we have counts for
105 papers
On Natural Groups
Oliver Knill
A group (G,*) is natural if its group operation is uniquely determined by a metric structure (G,d) on G in the following sense: every group structure (G,.) for which all right tran…
Elements of finite geometry I
Oliver Knill
This is a snapshot of a first part on a possibly much longer text on finite geometries, meaning graphs or finite abstract simplicial complexes. In in this first batch we review 12…
Euler Characteristics of Random Manifolds
Oliver Knill
We prove that the expectation of the Euler characteristic X(H) of random level surface H in a given simplicial complex G is E[X(H)] =2-2K(G)-X(G), where K(G)=1-f_0/2+f_1/3- ... is…
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…