Unitary Whitehead conjecture

Establish the unitary-calculus analogue of the Whitehead conjecture: prove that the unitary tower of U(V) at V=\mathbb{C} forms an exact complex analogous to the complex arising from the Goodwillie tower of S^1, and determine the resulting approximations \Omega P_{p^k}U(\mathbb{C}).

Background

The paper proposes applying unitary calculus to Neisendorfers spectral-sequence problem for the filtration of U(\infty). The required input is a bu-Whitehead conjecture involving spectra A_m, which are intended to play the role of symmetric product spectra. The conjectural exactness and the associated approximation model remain unresolved.

References

This is the content of the $bu$-Whitehead conjecture , which predicts that the unitary tower of $U(V)$ at $V=\mathbb{C}$ fits into an exact complex analogous to the one arising from the Goodwillie tower of $S1$.

— An abelian model for the Goodwillie tower of the circle  (2609.31269 - Nervo, 25 Sep 2026) in Section 5, subsection “Unitary Whitehead conjecture”