Although Alfred North Whitehead probably did not know of the new quantum theory of Heisenberg, Schrödinger and Dirac, there seem to be deep similarities between his idea of the process and the ideas of quantum theory. Both Whitehead’s metaphysics and quantum theory are theories of observations: The realities which quantum theory deals with are certain observations by scientists who use the theo...

We show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and nilpotent algebras. The classical First and Second Whitehead Lemmata state that the first, respectively second, cohomology group of a finite-dimensional semisimpl...

I. Review: An obstruction theory. — Let Θn be the group of diffeomorphism classes of oriented smooth homotopy spheres of dimension n. Let Diff(Sn−1) be the simplicial group of orientation preserving diffeomorphisms Sn−1 → Sn−1. For n > 5, the natural homomorphism from π0Diff(Sn−1) to Θn is surjective by Smale’s h–cobordism theorem, and injective by Cerf’s pseudo–isotopy theorem. It is easily se...

By applying an algorithm of Stallings regarding separability of elements in a free group, we give an alternative approach to that of Osborne and Zieschang in describing all primitive elements in the free group of rank 2. As a result, we give a proof of a classical result of Nielsen, used by Osborne and Zieschang in their work, that the only automorphisms of F2 that act trivially on the abeliani...