We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.

We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.’s of size ≥ א2 have nonfree Whitehead modules even though they are not complete discrete valuation rings. A module M is a Whitehead module if ExtR(M,R) = 0. The second author proved that the problem of whether every Whitehead Z-module is free is independent of ZFC + GCH (cf. [5], ...

In 1945, R. Fox introduced the so-called Fox torus homotopy groups in which the usual homotopy groups are embedded and their Whitehead products are expressed as commutators. A modern treatment of Fox torus homotopy groups and their generalization has been given and studied. In this note, we further explore these groups and their properties. We discuss co-multiplications on Fox spaces and Jacobi...

What is it famous for? The Whitehead Institute is probably one of those places that's famous for being famous. But that's not to say it doesn't deserve its reputation. Despite its relatively small staff — only 15 scientists are on the faculty — the Whitehead has a publication record that puts it among the top research institutions in genetics and molecular biology. What's its focus? Work there ...

We analyze the homological behavior of the attaching maps in the 2-local Goodwillie tower of the identity evaluated at S1 . 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 to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie...