Abstract Concepts of mutual interdependence, process, creative advance, and God occupy key areas in the philosophy Alfred North Whitehead. Process metaphysics lays emphasis on a naturalism rigorous rational empirical methodology with far-reaching implications. thinkers have compared Whiteheadian thought to Buddhism, Christianity, many other religions. However, African religious beliefs yet be c...

We give an explicit formula for Whitehead group of a threedimensional crystallographic group Γ in terms of the Whitehead groups of the virtually infinite cyclic subgroups of Γ. 0 Introduction The K-theory of integral group rings of crystallographic groups has been studied by Connolly and Koźniewski [8], Farrell and Hsiang [10], Farrell and Jones [11], Lück and Stamm [15], Quinn [20], Tsapogas [...

Firms that operate in the telecommunications industry often have to make large and risky investments in digital infrastructure. This paper examines how firm size affects the incentive to invest in infrastructure projects in industry environments that incur substantial network externalities. We suggest that, in the presence of network externalities, a firm's rate of growth first declines and the...

We study Whitehead products in the rational homotopy groups of a general component of a function space. For the component of any based map f : X → Y , in either the based or free function space, our main results express the Whitehead product directly in terms of the Quillen minimal model of f . These results follow from a purely algebraic development in the setting of chain complexes of derivat...

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We analyze the homological behavior of the attaching maps in the 2-local Good-willie tower of the identity evaluated at S 1. We show that they exhibit the same homological behavior as the James-Hopf maps used by N. Kuhn to prove the 2-primary Whitehead conjecture. We use this t...

In this paper we discuss several heuristic strategies which allow one to solve the Whitehead’s minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most non-minimal elements in a free group can be reduced...

A (right R-) module N is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module M , ExtR(M,N) = 0 implies M is projective. Dually, i-test modules are defined. For example, Z is a p-test abelian group iff each Whitehead group is free. Our first main result says that if R is a right hereditary non-right perfect ring, then the existence of p-test mo...